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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A346542 #16 Sep 18 2021 04:20:11
%S A346542 3,15,55,26607,209787,819739
%N A346542 Numbers k such that 5*2^k + 1 is an elite prime (A102742).
%C A346542 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.
%C A346542 a(7) > 9*10^6.
%H A346542 Alexander Aigner, <a href="https://doi.org/10.1007/BF01298923">Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind</a>, Monatsh. Math., Vol. 101 (1986), pp. 85-93; <a href="https://eudml.org/doc/178266">alternative link</a>.
%o A346542 (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;
%Y A346542 Subsequence of A002254.
%Y A346542 Cf. A102742.
%K A346542 nonn,hard,more
%O A346542 1,1
%A A346542 _Arkadiusz Wesolowski_, Sep 16 2021