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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..22.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A351541 A023697 A038468 * A303123 A043471 A203857

Adjacent sequences: A131345 A131346 A131347 * A131349 A131350 A131351

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 29 2007

Extensions

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

Status

approved