A187849 Integers k such that 2^(k-1) == 1 (mod k) and 2^(m-1) == 1 (mod m), where m is defined as m = k*(A000265(k-1) - 1) + 1.

563, 1291, 1733, 1907, 2477, 2609, 2693, 2837, 3533, 3677, 4157, 4517, 5693, 12809, 15077, 19997, 25603, 28517, 29573, 29837, 31517, 32237, 32717, 34949, 37277, 43613, 43973, 44453, 50333, 52253, 62477, 68213, 69197, 72893, 74717

Offset

1,1

Comments

The first condition of the definition means terms k are either primes or Fermat pseudoprimes to base 2 (see A001567). If the parameter m is also prime or Fermat pseudoprime to base 2, then k belongs to this sequence.

Composites in this sequence: 1771946607940820033, 14356915031659973281, ... - Max Alekseyev

If k = 1 and p is a composite number, then p == 0 (mod 3). (Is this heuristics or strict? - R. J. Mathar, Apr 04 2011) Terms to illustrate these cases:

k = 1291 = 2 * 645 + 1; p = 645 = 215 * 3.

k = 25603 = 2 * 12801 + 1; p = 12801 = 4267 * 3.

k = 424843 = 2 * 212421 + 1; p = 212421 = 70807 * 3.

k = 579883 = 2 * 289941 + 1; p = 289941 = 96647 * 3.

k = 4325443 = 2 * 2162721 + 1; p = 2162721 = 720907 * 3.

Links

Alzhekeyev Ascar M, Table of n, a(n) for n = 1..2297

Maple

isA187849 := proc(n) local redn, k, p, m; if modp(2^(n-1), n) = 1 then redn := n-1 ; k := A007814(redn) ; p := (n-1)/2^k ; m := n*(p-1)+1 ; is( modp(2^(m-1), m) = 1 ); else false; end if; end proc:
for n from 1 do if isA187849(n) then print(n); end if; end do: # R. J. Mathar, Mar 30 2011

Crossrefs

Sequence in context: A232679 A135437 A142759 * A237029 A183732 A014361

Adjacent sequences: A187846 A187847 A187848 * A187850 A187851 A187852

Keyword

nonn

Author

Alzhekeyev Ascar M, Mar 14 2011

Extensions

Edited by Max Alekseyev, Jun 04 2011

Status

approved