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 A263725 Smallest prime q > prime(n+3) such that the number p = prime(n)^2 + prime(n+1)^2 + prime(n+2)^2 + prime(n+3)^2 + q^2 is also prime. 1
 13, 17, 37, 31, 31, 37, 41, 41, 43, 47, 59, 61, 89, 79, 71, 79, 79, 89, 97, 109, 127, 107, 109, 109, 113, 139, 131, 139, 151, 149, 157, 157, 173, 181, 173, 191, 191, 193, 197, 223, 199, 211, 233, 239, 229, 233, 263, 257, 263, 271, 271, 277, 271, 281, 281, 293, 293, 311, 349, 317, 353, 331, 353, 353, 359, 419, 359, 419, 379, 419, 397, 401, 431, 409, 409, 433, 461, 443, 487, 449, 541, 487, 463, 569, 479, 467, 487, 491, 503 (list; graph; refs; listen; history; text; internal format)
 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 Wikipedia, Schinzel's Hypothesis H 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 Cf. A263724. Sequence in context: A126808 A053009 A069485 * A174056 A307894 A322472 Adjacent sequences:  A263722 A263723 A263724 * A263726 A263727 A263728 KEYWORD nonn AUTHOR Jonathan Sondow, Oct 24 2015 STATUS approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)