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

1,1

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

Links

Table of n, a(n) for n=1..35.

Example

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.

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]]}]

Crossrefs

Cf. A098268, A103579, A186283.

Sequence in context: A242840 A081081 A111111 * A161014 A344768 A363027

Adjacent sequences: A185340 A185341 A185342 * A185344 A185345 A185346

Keyword

easy,nonn

Author

Bill McEachen, Feb 26 2011

Status

approved