A282353 Primes p = x^2 + y^2 such that x + y is a perfect square.

41, 53, 313, 317, 337, 353, 373, 397, 457, 577, 1201, 1213, 1381, 1621, 2213, 3461, 3593, 3701, 3761, 4481, 4793, 5021, 5393, 5801, 7321, 7333, 7433, 7541, 7741, 7933, 8081, 8161, 8521, 9181, 9433, 10133, 10601, 11833, 12421, 13933, 14281, 14293, 14321, 14341, 14401, 14461, 14593

Offset

1,1

Comments

Least prime in which either x&y is k: 577, 53, 13933, 41, 41, 397, 53, 353, 337, etc. - Robert G. Wilson v, Feb 13 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

Prime number 53 is a term because 53 = 2^2 + 7^2 and 2 + 7 = 9 is a perfect square.

Mathematica

fQ[n_] := Block[{x = 1, y, lmt = Sqrt[n/2]}, While[y = Sqrt[n - x^2]; x < lmt && (!IntegerQ@ y || !IntegerQ@ Sqrt[x + y]), x++]; x < lmt]; Select[ Prime @Range@1750, fQ] (* Robert G. Wilson v, Feb 13 2017 *)

Prog

(PARI) is(p)=p%4==1 && isprime(p) && issquare(vecsum(qfbsolve(Qfb(1, 0, 1), p))) \\ Charles R Greathouse IV, Feb 14 2017

Crossrefs

Cf. A002313, A282381.

Sequence in context: A176924 A115663 A367421 * A118636 A116345 A127333

Adjacent sequences: A282350 A282351 A282352 * A282354 A282355 A282356

Keyword

nonn

Author

Altug Alkan, Feb 13 2017

Status

approved