A273236 Primes p such that p + k is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3.

563047, 1186631, 1205647, 1421647, 1871503, 2058047, 2615047, 2739103, 2795047, 3703463, 3743647, 4106447, 4723847, 4748047, 4758847, 5744447, 6991847, 8376847, 9951047, 10014847, 12214303, 12773447, 14161183, 14402447, 15232031, 15630847

Offset

1,1

Comments

All terms of this sequence are the sum of 4 but no fewer nonzero squares.

Links

Table of n, a(n) for n=1..26.

Example

The prime 563047 is a term because 563048 = 218^2 + 718^2, 563049 = 165^2 + 732^2 = 357^2 + 660^2 and 563050 = 71^2 + 747^2 = 141^2 + 737^2 = 505^2 + 555^2.

Prog

(PARI) is(n, k) = {nb = 0; lim = sqrtint(n); for (x=1, lim, if ((n-x^2 >= x^2) && issquare(n-x^2), nb++); ); nb == k; }
isok(n) = isprime(n) && is(n+1, 1) && is(n+2, 2) && is(n+3, 3);

Crossrefs

Cf. A025284, A025285, A025286, A273318.

Sequence in context: A124514 A100416 A151878 * A237935 A237693 A156412

Adjacent sequences: A273233 A273234 A273235 * A273237 A273238 A273239

Keyword

nonn

Author

Altug Alkan, May 26 2016

Status

approved