This article is under construction.
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
|
..., 5, 7, 9, 11, 13, 15, 17, 19, 21, ...
|
A005408
|
Prime numbers
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
|
A000040
|
Lucas numbers
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2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...
|
A000032
|
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
|
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
|
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
|
A011292
|
11 8
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214358881
|
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1.30529988
|
A011293
|
11 9
|
2357947691
|
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1.27098161
|
A011294
|
11 10
|
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.
|
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
|
3 11
|
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
|
|
1.72971580
|
A154176
|
4 11
|
4194304
|
|
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0.67118774
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A153269
|
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1.48989610
|
A154177
|
5 11
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48828125
|
|
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0.74722173
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A153586
|
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1.33829083
|
A154178
|
6 11
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362797056
|
|
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0.81150756
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A153621
|
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1.23227440
|
A154179
|
7 11
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1977326743
|
|
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0.86719447
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A153791
|
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1.15314387
|
A154180
|
8 11
|
8589934592
|
|
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0.91631381
|
A154011
|
|
1.09132916
|
A154181
|
9 11
|
31381059609
|
|
|
0.96025256
|
A154161
|
|
1.04139268
|
A154182
|
10 11
|
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).
|
11!
|
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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|
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12
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|
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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
|
8
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9
|
10
|
11
|
12 through 36
|
Representation
|
1011
|
102
|
23
|
21
|
15
|
14
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13
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12
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11
|
10
|
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