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.

A165966 Triangular numbers that are sums of twin prime pairs.

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%I A165966 #14 Dec 27 2019 11:55:54
%S A165966 36,120,276,300,2556,3240,5460,8256,12720,23436,26796,34980,41616,
%T A165966 46056,56616,59340,103740,122760,139656,147696,157080,185136,195000,
%U A165966 231540,277140,333336,353220,386760,401856,516636,609960,860016,1001820
%N A165966 Triangular numbers that are sums of twin prime pairs.
%C A165966 All terms are multiples of 12.
%H A165966 Amiram Eldar, <a href="/A165966/b165966.txt">Table of n, a(n) for n = 1..10000</a>
%F A165966 a(n) = A105174(n)*(A105174(n) + 1)/2.
%e A165966 36 = 8*9/2 is a term since it is triangular and the sum of the twin primes 17 and 19.
%e A165966 120 = 15*16/2 is a term since it is triangular and the sum of the twin primes 59 and 61.
%t A165966 tri[n_] := n*(n+1)/2; Select[tri /@ Range[10^3], And @@ PrimeQ[#/2 + {-1, 1}] &] (* _Amiram Eldar_, Dec 27 2019 *)
%o A165966 (PARI) lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg, ", ")););} \\ _Michel Marcus_, Oct 16 2013
%Y A165966 Subsequence of A111163 and of A054735.
%Y A165966 Cf. A000217, A001359, A105174.
%K A165966 nonn
%O A165966 1,1
%A A165966 _Zak Seidov_, Oct 01 2009