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.
%I A365098 #22 May 06 2024 01:47:44
%S A365098 2,11,971
%N A365098 Primes p such that Sum_{k=1..p-1} q^2_p(k) == 0 (mod p), with q_p(k) a Fermat quotient.
%C A365098 The congruence in the definition is given in Gy, 2018, Eq. 16.
%C A365098 The terms, except for the prime 2, satisfy the congruence B_{p-1} - 1 + 1/p == (B_{2p-2} - 1 + 1/p)/2 (mod p^2), with B_i a Bernoulli number (cf. Gy, 2018, Eq. 18).
%C A365098 Any odd prime that is a term of both A007540 and A197632, i.e., that is simultaneously a Wilson prime and a Lerch prime, is in this sequence (cf. Gy, 2018, Theorem 5).
%C A365098 An equivalent definition, better suited for computational purposes, is: "Primes p such that Sum_{k=1..p-1} (k^(p-1) - 1)^2 == 0 (mod p^3)." - _John Blythe Dobson_, Apr 30 2024
%C A365098 a(4) > 427000, if it exists (Gy, 2018). - _Amiram Eldar_, Aug 22 2023
%C A365098 a(4) > 39540000, if it exists. - _John Blythe Dobson_, Apr 30 2024
%H A365098 René Gy, <a href="http://math.colgate.edu/~integers/s10/s10.Abstract.html">Generalized Lerch primes</a>, INTEGERS, 18 (2018), #A10.
%t A365098 Join[{2}, Select[Prime[Range[2, 200]], Divisible[Numerator[BernoulliB[# - 1] - 1 + 1/# - (BernoulliB[2*# - 2] - 1 + 1/#)/2], #^2] &]] (* _Amiram Eldar_, Aug 22 2023 *)
%o A365098 (PARI) forprime(p = 2, 10000, if(sum(j=1, p-1, (Mod(j, p^3)^(p-1) - 1)^2) % p^3 == 0, print1(p, ", "))) /* _John Blythe Dobson_, Apr 30 2024 */
%Y A365098 Cf. A007540, A197632.
%K A365098 nonn,hard,more,bref
%O A365098 1,1
%A A365098 _Felix Fröhlich_, Aug 21 2023