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 A256147 #16 Apr 02 2015 04:10:38 %S A256147 1,1,2,1,3,1,4,2,7,3,2,6,2,1,7,7,7,17,7,3,1,43,66,2,72,51,7,50,32,3, %T A256147 111,85,26,1,44,31,7,7,96,157,23,1,88,3,97,7 %N A256147 First repeated number in Sylvester's sequence modulo prime(n). %C A256147 Sylvester's sequence (A000058) is an infinite coprime sequence, a fact that may lead to the incorrect intuition that all primes occur as factors of its terms. It's quite easy to check that no multiple of 5 occurs, since Sylvester's sequence modulo 5 is 2, 3, 2, 3, 2, 3, ... %C A256147 If a multiple of p occurs in Sylvester's sequence at position j, then A000058(k) == 1 (mod p) for all k > j. %C A256147 But if no multiple of p occurs in Sylvester's sequence at all, then Sylvester's sequence is fully periodic modulo p or it enters a cycle at some point. %D A256147 J. J. Sylvester, Postscript to Note on a Point in Vulgar Fractions. American Journal of Mathematics Vol. 3, No. 4 (Dec., 1880): 388 - 389. %e A256147 a(4) = 1, because the fourth prime is 7 and Sylvester's sequence modulo 7 is 2, 3, 0, 1, 1, 1, ... %e A256147 a(5) = 3, because the fifth prime is 11 and Sylvester's sequence modulo 11 is 2, 3, 7, 10, 3, 7, 10, 3, 7, 10, ... (3 is the first number repeated). %Y A256147 Cf. A007996, A126263, A255595. %K A256147 nonn %O A256147 1,3 %A A256147 _Alonso del Arte_, Mar 16 2015