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
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.
Programs
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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]]}]
Comments