OFFSET
2,1
COMMENTS
The corresponding primes p form A263724.
The prime q exists for all n > 1 under Schinzel's Hypothesis H; see Sierpinski (1988), p. 221.
REFERENCES
W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988.
LINKS
EXAMPLE
The primes 373 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2, 653 = 5^2 + 7^2 + 11^2 + 13^2 + 17^2, and 1997 = 7^2 + 11^2 + 13^2 + 17^2 + 37^2 lead to a(2) = 13, a(3) = 17, and a(4) = 37.
MATHEMATICA
Table[k = 4;
While[! PrimeQ[Sum[Prime[n + j]^2, {j, 0, 3}] + Prime[n + k]^2], k++];
Prime[n + k], {n, 2, 90}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Oct 24 2015
STATUS
approved