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 A245206 #20 Jul 09 2025 01:54:43
%S A245206 1019
%N A245206 Odd primes p with E_{p-3}(1/4) == 0 (mod p), where E_n(x) denotes the Euler polynomial of degree n.
%C A245206 The conjecture in A245204 asserts that the current sequence contains infinitely many primes.
%C A245206 Our computation shows that the second term should be greater than prime(2600) = 23321.
%H A245206 Zhi-Wei Sun, <a href="http://dx.doi.org/10.1007/s11425-011-4302-x">Super congruences and Euler numbers</a>, Sci. China Math., Vol. 54, No. 12 (2011), 2509-2535; <a href="https://arxiv.org/abs/1001.4453">arXiv preprint</a>, arXiv:1001.4453 [math.NT], 2010-2011.
%H A245206 <a href="/index/O#oneterm">Index entries for one-term sequences</a>.
%e A245206 a(1) = 1019 since 1019 is a prime with E_{1019-3}(1/4) == 88*1019 (mod 1019^2).
%t A245206 rMod[m_,n_]:=Mod[Numerator[m]*PowerMod[Denominator[m],-1,n],n,-n/2]
%t A245206 n=0;Do[If[rMod[EulerE[Prime[k]-3,1/4],Prime[k]]==0,n=n+1;Print[n," ",Prime[k]]],{k,2,200}]
%Y A245206 Cf. A000040, A001586, A122045, A198245, A245089, A245204.
%K A245206 nonn,more,hard,bref
%O A245206 1,1
%A A245206 _Zhi-Wei Sun_, Jul 13 2014