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.

A131348 Sum of squares of prime quadruplets.

This page as a plain text file.
%I A131348 #13 May 13 2017 12:41:33
%S A131348 364,940,44140,152140,2722540,8820940,14062540,17388940,42380140,
%T A131348 48024940,127916140,356076940,676520140,979064140,990360940,
%U A131348 1032336940,1302488140,1431108940,1509322540,1766520940,1984702540,2561372140
%N A131348 Sum of squares of prime quadruplets.
%C A131348 This is to prime quadruplets A007530 as sums of squares of twin primes A063533 are to twin primes. This is to prime quadruplets A007530 as A133524 is to four consecutive primes. Note that prime quadruplets are not the same as four consecutive primes. After a(1) these are always multiples of 20, because after A007530(1) = 5, all A007530(n) == 1 mod 10. a(n) is a prime times 20 for an = 1, 2, 3, 12, 16, 21.
%F A131348 a(n) = p^2 + (p+2)^2 + (p+6)^2 + (p+8)^2 for p in A007530.
%e A131348 a(1) = 364 = 5^2 + 7^2 + 11^2 + 13^2.
%e A131348 a(2) = 940 = 11^2 + 13^2 + 17^2 + 19^2.
%e A131348 a(3) = 44140 = 101^2 + (103)^2 + (107)^2 + (109)^2 because 101, 103, 107, 109 are a prime quadruplet.
%t A131348 Total[#^2]&/@Select[Partition[Prime[Range[3000]],4,1],MatchQ[#,{#[[1]],#[[1]]+2,#[[1]]+6,#[[1]]+8}]&]  (* _Harvey P. Dale_, Feb 03 2011 *)
%Y A131348 Cf. A000040, A007530, A063533, A133523, A133524.
%K A131348 easy,nonn
%O A131348 1,1
%A A131348 _Jonathan Vos Post_, Sep 29 2007
%E A131348 Corrected and extended by _Harvey P. Dale_, Feb 03 2011