A185343 Least positive number k such that k*p+1 divides 2^p+1 where p is prime(n), or 0 if no such number exists.

2, 0, 2, 6, 62, 210, 2570, 9198, 121574, 2, 23091222, 48, 2, 68186767614, 6, 2, 48, 12600235023025650, 109368, 794502, 24, 2550476412689091085878, 6, 2, 10, 8367330694575771627040945250, 4030501264, 6, 955272, 2, 446564785985483547852197647548252246, 8, 8, 32424, 8

Offset: 1

Author

Bill McEachen, Feb 26 2011

Keywords

• easy
• nonn

Comments

Akin to A186283 except for 2^p+1 and restricted to primes.

The larger terms of this sequence occur for the primes p > 3 in sequence A000978. These large terms are (2^p-2)/(3p).

a(n) = 2 iff prime(n) is in A103579. - Robert Israel, Jul 17 2023

Examples

			2^3+1 = 9 has no factor of the form k*3+1 except 1, so a(primepi(3)) = a(2) = 0.
2^29+1 = 536870913 has factor 2*29+1=59, so a(primepi(29)) = a(10) = 2.
		

Crossrefs

Cf. A098268, A103579, A186283.

Programs

Maple

f:= proc(n) local p,F;
  p:= ithprime(n);
  F:= select(t -> t mod p = 1, numtheory:-divisors(2^p+1) minus {1});
  if F = {} then 0 else (min(F)-1)/p; fi
end proc:
map(f, [$1..50]); # Robert Israel, Jul 17 2023

Mathematica

Table[q = First /@ FactorInteger[2^p + 1]; s = Select[q, Mod[#1, p] == 1 &, 1]; If[s == {}, 0, (s[[1]] - 1)/p], {p, Prime[Range[30]]}]