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11

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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 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... A000040
Lucas numbers 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... A000032
Jacobsthal numbers 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ... A001045

In Pascal's triangle, 11 occurs twice. (In Lozanić's triangle, 11 occurs four times).

Sequences pertaining to 11

Multiples of 11 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, ... A008593
Fermat pseudoprimes to base 11 10, 15, 70, 133, 190, 259, 305, 481, 645, 703, 793, ... A020139
sequence beginning at 9 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, ... A033478
sequence beginning at 11 11, 56, 28, 14, 7, 36, 18, 9, 46, 23, 116, 58, 29, 146, ... A259193
11-rough numbers 1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, ... 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.

3.31662479 A010468 11 2 121
2.22398009 A010583 11 3 1331
1.82116028 A011008 11 4 14641
1.61539426 A011096 11 5 161051
1.49130147 A011290 11 6 1771561
1.40854388 A011291 11 7 19487171
1.34950371 A011292 11 8 214358881
1.30529988 A011293 11 9 2357947691
1.27098161 A011294 11 10 25937424601
1.24357522 A011295 11 11 285311670611
A001020

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 A152748 3.45943161 A020863 2 11 2048
0.41703239 2.39789527 A016634 59874.14171519
0.45815690 A152974 2.18265833 A154175 3 11 177147
0.47738944 2.09472584 294204.01797389
0.57812965 A153104 1.72971580 A154176 4 11 4194304
0.67118774 A153269 1.48989610 A154177 5 11 48828125
0.74722173 A153586 1.33829083 A154178 6 11 362797056
0.81150756 A153621 1.23227440 A154179 7 11 1977326743
0.86719447 A153791 1.15314387 A154180 8 11 8589934592
0.91631381 A154011 1.09132916 A154181 9 11 31381059609
0.96025256 A154161 1.04139268 A154182 10 11 100000000000

Values for number theoretic functions with 11 as an argument

–1
–2
5
12
2
10
1
1
10 This is the Carmichael lambda function.
–1 This is the Liouville lambda function.
1.0004941886041194645587... (see A013669).
11! 39916800
3628800

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −11, 11

Both and are unique factorization domains.

1 Unit
2 Prime
3 Prime
4 2 2
5
6
7 Prime
8 2 3
9 3 2
10
11
12
13 Prime
14 2 × 7
15
16 2 4
17 Prime
18
19 Prime
20

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.

Prime
Prime
Prime and/or irreducible
Prime and/or irreducible
Prime and/or irreducible Prime
Prime

Representation of 11 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 through 36
Representation 1011 102 23 21 15 14 13 12 11 10 B

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

Some integers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
1729