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 A372525 #14 Jun 07 2024 04:31:26
%S A372525 6,1991,5459,17391
%N A372525 Composite numbers k that divide A000296(k) + (-1)^k.
%C A372525 Equivalently, composite numbers k such that Sum_{i=1..k-1} (-1)^i * Bell(i) == 1 (mod k), where Bell(i) = A000110(i).
%C A372525 The congruence holds for all the primes. This is a special case of Sun and Zagier's (2011) Theorem 1.1, when m = 1.
%C A372525 a(5) > 56000, if it exists.
%H A372525 Grzegorz Serafin, <a href="https://doi.org/10.36045/j.bbms.210412a">Backward Touchard congruence</a>, Bull. Belg. Math. Soc. Simon Stevin, Vol. 28, No. 4 (2022), pp. 603-614; <a href="https://arxiv.org/abs/2110.06129">arXiv preprint</a>, arXiv:2110.06129 [math.NT], 2021.
%H A372525 Zhi-Wei Sun and Don Zagier, <a href="https://doi.org/10.1017/S0004972711002218">On a curious property of Bell numbers</a>, Bulletin of the Australian Mathematical Society, Vol. 84, No. 1 (2011), pp. 153-158.
%t A372525 f[k_] := f[k] = Sum[Binomial[k-1, i] * f[k-i-1], {i, 1, k-1}]; f[0] = 1; Select[Range[2000], CompositeQ[#] && Divisible[f[#] + (-1)^# , #] &]
%Y A372525 Cf. A000110, A000296, A179508.
%K A372525 nonn,hard,more
%O A372525 1,1
%A A372525 _Amiram Eldar_, Jun 07 2024