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A131348
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Sum of squares of prime quadruplets.
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0
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364, 940, 44140, 152140, 2722540, 8820940, 14062540, 17388940, 42380140, 48024940, 127916140, 356076940, 676520140, 979064140, 990360940, 1032336940, 1302488140, 1431108940, 1509322540, 1766520940, 1984702540, 2561372140
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 A00753091) = 5, all A007530(n) == 1 mod 10. a(n) is a prime times 20 for an = 1, 2, 3, 12, 16, 21.
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FORMULA
| a(n) = p^2 + (p+2)^2 + (p+6)^2 + (p+8)^2 for p in A007530.
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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.
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MATHEMATICA
| Total[#^2]&/@Select[Partition[Prime[Range[3000]], 4, 1], MatchQ[#, {#[[1]], #[[1]]+2, #[[1]]+6, #[[1]]+8}]&] (* From Harvey P. Dale, Feb. 3, 2011 *)
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CROSSREFS
| Cf. A000040, A007530, A063533, A133523, A133524.
Sequence in context: A004534 A023697 A038468 * A043471 A203857 A105920
Adjacent sequences: A131345 A131346 A131347 * A131349 A131350 A131351
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 29 2007
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, Feb. 3, 2011
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