A244031 Integers n>1 such that the quadratic form x^2+n*y^2 does not represent a prime strictly between n and 2n.

3, 5, 8, 11, 17, 23, 24, 26, 29, 35, 41, 56, 59, 68, 83, 89, 107, 119, 120, 125, 134, 179, 185, 194, 206, 251, 263, 269, 290, 293, 314, 326, 341, 356, 371, 389, 401, 404, 461, 464, 479, 489, 491, 524, 545, 569, 593, 626

Offset: 1

Author

N. J. A. Sloane, Jun 22 2014

Keywords

• nonn

Comments

Or: Positive numbers n such that n + k^2 is composite for all 1 <= k^2 <= n.

The next term a(105), if it exists, is > 156*10^6. - M. F. Hasler, May 07 2018

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..104 (cf. Jagy & Kaplansky).
• William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy]

Crossrefs

Union of A244029 (subsequence of primes) and A244030 (composite terms).

Programs

PARI

is(n)=!for(k=1,sqrtint(n),isprime(n+k^2)&&return) \\ M. F. Hasler, May 07 2018

Extensions

Added "n>1" as suggested by David J. Seal. - N. J. A. Sloane, May 19 2018