OFFSET
2,1
COMMENTS
The corresponding prime q is in A263725.
The prime p exists for all n > 1 under Schinzel's Hypothesis H; see Sierpinski (1988), p. 221.
If q = prime(n+4), then p is in A133559 (prime sums of squares of 5 consecutive primes). The converse holds if a(n) != a(m) when n != m (which holds if a(n) < a(n+1), as appears to be true).
REFERENCES
W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988; see p. 221.
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(1) = 373, a(2) = 653, and a(3) = 1997.
MATHEMATICA
Table[k = 4;
While[p = Sum[Prime[n + j]^2, {j, 0, 3}] + Prime[n + k]^2; ! PrimeQ[p],
k++]; p, {n, 2, 60}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Oct 24 2015
STATUS
approved