A133524 -id:A133524 - cp's OEIS frontend

A131348 Sum of squares of prime quadruplets.

364, 940, 44140, 152140, 2722540, 8820940, 14062540, 17388940, 42380140, 48024940, 127916140, 356076940, 676520140, 979064140, 990360940, 1032336940, 1302488140, 1431108940, 1509322540, 1766520940, 1984702540, 2561372140

Offset: 1

Jonathan Vos Post, Sep 29 2007

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.

			a(1) = 364 = 5^2 + 7^2 + 11^2 + 13^2.
a(2) = 940 = 11^2 + 13^2 + 17^2 + 19^2.
a(3) = 44140 = 101^2 + (103)^2 + (107)^2 + (109)^2 because 101, 103, 107, 109 are a prime quadruplet.

Cf. A000040, A007530, A063533, A133523, A133524.

Total[#^2]&/@Select[Partition[Prime[Range[3000]],4,1],MatchQ[#,{#[[1]],#[[1]]+2,#[[1]]+6,#[[1]]+8}]&]  (* Harvey P. Dale, Feb 03 2011 *)

a(n) = p^2 + (p+2)^2 + (p+6)^2 + (p+8)^2 for p in A007530.

Corrected and extended by Harvey P. Dale, Feb 03 2011

cp's OEIS Frontend

A131348 Sum of squares of prime quadruplets.

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