cp's OEIS Frontend

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.

A316111 a(n) is the smallest k > 1 such that gcd(k, n^k - n) = 1, for n > 1.

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%I A316111 #52 Aug 13 2018 15:33:14
%S A316111 35,35,77,77,143,55,55,77,119,119,35,55,187,143,77,35,35,77,143,247,
%T A316111 95,35,77,77,77,55,55,143,77,77,35,35,247,143,143,35,35,77,77,143,55,
%U A316111 95,119,119,77,35,55,143,143,77,35,35,119,299,221,55,35,77,77,77,55,55,187,119
%N A316111 a(n) is the smallest k > 1 such that gcd(k, n^k - n) = 1, for n > 1.
%C A316111 Conjecture: all the terms are in A121707. If k is a term, then k is an "anti-Carmichael number": p-1 does not divide k-1 for every prime p dividing k.
%C A316111 The sequence is unbounded, since a(m!) > m.
%C A316111 Prediction: a(n) < n for all sufficiently large n.
%C A316111 GCD(n, a(n)) = 1. a(n) is odd. Is a(n) squarefree? - _David A. Corneth_, Aug 13 2018
%o A316111 (PARI) a(n) = {my(k=2); while (gcd(k, n^k - n) != 1, k++); k;} \\ _Michel Marcus_, Aug 13 2018
%o A316111 (PARI) a(n) = {my(k=3); while (gcd(k, n^k - n) != 1, k+=2; while(gcd(n, k) > 1, k+=2)); k} \\ _David A. Corneth_, Aug 13 2018
%Y A316111 Cf. A121707, A267999.
%K A316111 nonn
%O A316111 2,1
%A A316111 _Thomas Ordowski_, Aug 13 2018
%E A316111 More terms from _Michel Marcus_, Aug 13 2018