A374976 Odd k with p^k mod k != p for all primes p.

1, 9, 27, 63, 75, 81, 115, 119, 125, 189, 207, 209, 215, 235, 243, 279, 299, 319, 323, 387, 407, 413, 423, 515, 517, 531, 535, 551, 567, 575, 583, 611, 621, 623, 667, 675, 707, 713, 729, 731, 747, 767, 779, 783, 799, 815, 835, 851, 869, 893, 899, 917, 923, 927

Offset

1,2

Comments

Alternatively: 1, and odd composites not a pseudoprime to any prime base.

The sequence contains no primes, no pseudoprimes to any prime base (A001567, A005935, A005936, A005938, A020139, A020141...), and no Carmichael numbers (A002997).

Links

Francois R. Grieu, Table of n, a(n) for n = 1..10000

Example

k=3 (resp. 5, 7) is not in the sequence because for prime p=2 it holds p^k mod k = 2 which is p.
k=9 is in the sequence because for prime p=2 (resp. 3, 5, 7) it holds p^k mod k = 8 (resp. 0, 8, 1) which is not p, and for all other primes p it holds p>=k therefore p^k mod k can't be p.

Mathematica

Cases[Range[1, 930, 2], k_/; (For[p=2, p<k && PowerMod[p, k, k]!=p, p=NextPrime[p]]; p>=k)]

Crossrefs

Cf. A000040, A001567, A005935, A005936, A005938, A020139, A020141, A020145, A002997.

Sequence in context: A158926 A112524 A254622 * A340119 A271990 A153237

Adjacent sequences: A374973 A374974 A374975 * A374977 A374978 A374979

Keyword

nonn

Author

Francois R. Grieu, Jul 26 2024

Status

approved