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.

A322155 Consecutive terms that appear more than once in A014237.

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%I A322155 #67 Dec 27 2018 13:58:58
%S A322155 -1,5,13,41,67,131,167,191,199,319,433,503,667,685,835,859,1033,1565,
%T A322155 1645,2087,2695,2969,3199,3329,3743,3949,4135,4625,4639,4831,5549,
%U A322155 5629,5663,5741,5807,6031,6749,7171,7543,8621,8773,9161,9293,10049,10333,11773,12061,13057
%N A322155 Consecutive terms that appear more than once in A014237.
%C A322155 The only term that appears three times is -1, while all other terms appear twice (looking up to n = 10000 in A014237).
%C A322155 Conjecture: the sequence is infinite.
%e A322155 -1 is in the sequence since it appears three consecutive times in A014237 (at n = 2, 3, 4).
%e A322155 5 is in the sequence since it appears two consecutive times in A014237 (at n = 7, 8).
%t A322155 nonPrime[n_] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n];  diff[n_] := Prime[n] - nonPrime[n]; s={}; d1=0; n=3; While[Length[s] < 50, d2 = diff[n]; n++; If[d2 == d1, AppendTo[s, d1]]; d1 = d2]; s (* _Amiram Eldar_, Dec 12 2018 *)
%o A322155 (PARI) nextcomp(c) = {while(isprime(c), c++); c;}
%o A322155 lista(nn) = {my(p = 2, c = 1, d, v = vector(nn)); for (n=1, nn, v[n] = p - c; p = nextprime(p+1); c = nextcomp(c+1);); my(last = v[1], nb = 1); for (n=2, nn, if (v[n] == last, nb++, if (nb > 1, print1(last, ", ")); last = v[n]; nb = 1););} \\ _Michel Marcus_, Dec 20 2018
%Y A322155 Cf. A000040, A014237, A018252.
%K A322155 sign
%O A322155 1,2
%A A322155 _Enrique Navarrete_, Dec 11 2018