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 A193855 #51 Jun 05 2024 12:10:23
%S A193855 11,23,691
%N A193855 Primes p such that tau(p) is congruent to 1 (mod p), where tau is the Ramanujan tau function.
%C A193855 M. J. Hopkins wrote "It is not known whether or not tau(p) == 1 mod p holds for infinitely many primes". For more information about this open problem see the Sloane comment in A000594.
%C A193855 a(4) > 500000. - _Dana Jacobsen_, Sep 06 2015
%C A193855 a(4) > 10^7. - _Seiichi Manyama_, Nov 25 2017
%C A193855 Terms 23 and 691 are exceptional primes for Ramanujan's tau function, see A262339. - _Jud McCranie_, Nov 05 2020
%C A193855 A subset of A295645. - _Jud McCranie_, Nov 06 2020
%D A193855 M. J. Hopkins, Algebraic topology and modular forms, Proc. Internat. Congress Math., Beijing 2002, Vol. I, pp. 291-317.
%D A193855 M. J. Hopkins, Algebraic topology and modular forms, ICM 2002, Vol. I, pp. 283-309.
%H A193855 M. J. Hopkins, <a href="http://arxiv.org/abs/math/0212397">Algebraic topology and modular forms</a>, arXiv:math/0212397 [math.AT], 2002.
%H A193855 B. Mazur and A. Wiles, <a href="http://www.numdam.org/item?id=CM_1986__59_2_231_0">On p-adic analytic families of Galois representations</a>, Compositio Mathematica, tome 59, n. 2 (1986), p. 231-264.
%t A193855 Select[Prime[Range[1, 1000]], 1 == Mod[RamanujanTau[#], #] &] (* _Robert Price_, May 20 2015 *)
%o A193855 (Perl) use ntheory ":all"; forprimes { say if (ramanujan_tau($_) % $_) == 1; } 1000; # _Dana Jacobsen_, Sep 06 2015
%o A193855 (PARI) forprime(n=1,1000,if(Mod(ramanujantau(n),n)==1,print1(n,", "))) \\ _Dana Jacobsen_, Sep 06 2015
%Y A193855 Cf. A000594, A262339, A295645.
%K A193855 nonn,bref,hard,more
%O A193855 1,1
%A A193855 _Omar E. Pol_, Aug 14 2011