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

3, 15, 55, 26607, 209787, 819739

Offset: 1

Author

Arkadiusz Wesolowski, Sep 16 2021

Keywords

• nonn
• hard
• more

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

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

Crossrefs

Subsequence of A002254.

Cf. A102742.

Programs

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;