A346542 Numbers k such that 5*2^k + 1 is an elite prime (A102742).

3, 15, 55, 26607, 209787, 819739

Offset

1,1

Comments

An integer k is in this sequence if and only if there is no solution to the congruence x^2 == 2^(2^k) + 1 (mod p), where p is a prime of the form 5*2^k + 1.

a(7) > 9*10^6.

Links

Table of n, a(n) for n=1..6.

Alexander Aigner, Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind, Monatsh. Math., Vol. 101 (1986), pp. 85-93; alternative link.

Prog

(PARI) isok(k)=my(p=5*2^k+1); k>2 && Mod(k, 2)==1 && Mod(3, p)^((p-1)/2)+1==0 && kronecker(lift(Mod(2, p)^2^k)+1, p)==-1;

Crossrefs

Subsequence of A002254.

Cf. A102742.

Sequence in context: A084175 A081951 A367520 * A033853 A284014 A049187

Adjacent sequences: A346539 A346540 A346541 * A346543 A346544 A346545

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Sep 16 2021

Status

approved