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
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
KEYWORD
easy,nonn
AUTHOR
Bill McEachen, Feb 26 2011
STATUS
approved