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Please do not rely on any information it contains.
11 is an integer with the largest known multiplicative persistence in base 10 (A003001, A031346).
Membership in core sequences
Odd numbers
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..., 5, 7, 9, 11, 13, 15, 17, 19, 21, ...
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A005408
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Prime numbers
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
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A000040
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Lucas numbers
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2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...
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A000032
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Jacobsthal numbers
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1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ...
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A001045
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In Pascal's triangle, 11 occurs twice. (In Lozanić's triangle, 11 occurs four times).
Sequences pertaining to 11
Multiples of 11
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0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, ...
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A008593
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Fermat pseudoprimes to base 11
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10, 15, 70, 133, 190, 259, 305, 481, 645, 703, 793, ...
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A020139
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sequence beginning at 9
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9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, ...
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A033478
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sequence beginning at 11
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11, 56, 28, 14, 7, 36, 18, 9, 46, 23, 116, 58, 29, 146, ...
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A259193
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11-rough numbers
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1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, ...
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A008364
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Partitions of 11
There are 56 partitions of 11.
Roots and powers of 11
In the table below, irrational numbers are given truncated to eight decimal places.
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3.31662479
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A010468
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11 2
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121
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2.22398009
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A010583
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11 3
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1331
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1.82116028
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A011008
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11 4
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14641
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1.61539426
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A011096
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11 5
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161051
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1.49130147
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A011290
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11 6
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1771561
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1.40854388
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A011291
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11 7
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19487171
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1.34950371
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A011292
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11 8
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214358881
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1.30529988
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A011293
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11 9
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2357947691
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1.27098161
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A011294
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11 10
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25937424601
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1.24357522
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A011295
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11 11
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285311670611
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A001020
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Logarithms and eleventh powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.
If is not a multiple of 23, then either or is. Hence the formula for the Legendre symbol .
As above, irrational numbers in the following table are truncated to eight decimal places.
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0.28906482
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A152748
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3.45943161
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A020863
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2 11
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2048
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0.41703239
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2.39789527
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A016634
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59874.14171519
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0.45815690
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A152974
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2.18265833
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A154175
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3 11
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177147
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0.47738944
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2.09472584
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294204.01797389
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0.57812965
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A153104
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1.72971580
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A154176
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4 11
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4194304
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0.67118774
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A153269
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1.48989610
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A154177
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5 11
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48828125
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0.74722173
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A153586
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1.33829083
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A154178
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6 11
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362797056
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0.81150756
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A153621
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1.23227440
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A154179
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7 11
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1977326743
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0.86719447
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A153791
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1.15314387
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A154180
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8 11
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8589934592
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0.91631381
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A154011
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1.09132916
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A154181
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9 11
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31381059609
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0.96025256
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A154161
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1.04139268
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A154182
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10 11
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100000000000
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Values for number theoretic functions with 11 as an argument
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–1
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–2
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5
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12
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2
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10
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1
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1
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10
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This is the Carmichael lambda function.
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–1
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This is the Liouville lambda function.
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1.0004941886041194645587... (see A013669).
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11!
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39916800
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3628800
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Factorization of some small integers in a quadratic integer ring adjoining the square roots of −11, 11
Both and are unique factorization domains.
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1
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Unit
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2
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Prime
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3
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Prime
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4
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2 2
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5
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6
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7
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Prime
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8
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2 3
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9
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3 2
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10
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11
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12
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13
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Prime
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14
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2 × 7
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15
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16
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2 4
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17
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Prime
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18
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19
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Prime
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20
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Factorization of 11 in some quadratic integer rings
As was mentioned above, 11 is a prime number in . But it is composite in some quadratic integer rings.
As was mentioned above, 11 is a prime number in . But it is composite in some quadratic integer rings.
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Prime
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Prime
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Prime and/or irreducible
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Prime and/or irreducible
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Prime and/or irreducible
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Prime
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Prime
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Representation of 11 in various bases
Base
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12 through 36
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Representation
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1011
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102
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23
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21
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15
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14
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13
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12
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11
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10
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B
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Clearly 11 is a palindromic number in base 10. However, and this may seem rather counter-intuitive, it is also a strictly non-palindromic number (A016038). As the chart above shows, it is not palindromic in binary, nor any other base up to base 9.
See also