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%I #24 Sep 04 2023 16:37:02
%S 373,653,5381,6701,8069,19541,24821,53549,56909,69389,93581,107741,
%T 131837,184901,196661,237821,252509,344021,370661,395069,498989,
%U 609269,783701,1055429,1174781,1239341,1492637,1576229,1713989,1749149,2024261
%N Primes which have a partition as the sum of squares of five consecutive primes.
%C For sums of squares of two consecutive primes, only 2^2 + 3^2 = 13 is prime.
%C For sums of squares of three consecutive primes (A133529), it seems that only 83 belonging (checked for starting primes prime(k) for all k < 1000000).
%C Sums of squares of four (and all even numbers of) consecutive primes are even numbers with the exception of 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.
%H Harvey P. Dale, <a href="/A133559/b133559.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)=373 because prime(2)^2 + prime(3)^2 + prime(4)^2 + prime(5)^2 + prime(6)^2 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373 is prime. [Corrected by _Jonathan Sondow_, Nov 04 2015]
%t b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
%t Select[Total/@Partition[Prime[Range[200]]^2,5,1],PrimeQ] (* _Harvey P. Dale_, Apr 07 2015 *)
%Y Cf. A133529, A133538, A133560.
%K nonn
%O 1,1
%A _Artur Jasinski_, Sep 16 2007