A165354 Primes p such that p+(p^2-1)/8 is an integer but not a prime number.

3, 5, 11, 13, 19, 29, 37, 43, 47, 53, 59, 61, 67, 83, 89, 97, 101, 107, 109, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 263, 269, 271, 277, 283, 293, 307, 313, 317, 331, 347, 349, 353, 359, 373, 379, 389

Offset: 1

Author

Vincenzo Librandi, Sep 16 2009

Keywords

• nonn
• easy

Comments

For p=2, p+(p^2-1)/8 is not integer; for all others, p=4k+-1, it is an integer.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A165352, A165353.

Programs

Magma

[p: p in PrimesUpTo(500)| not IsPrime(Floor(p+(p^2-1)/8))]; // Vincenzo Librandi, Sep 12 2013

Mathematica

Select[Prime[Range[2, 500]], ! PrimeQ[(#^2 - 1) / 8 + #]&] (* Vincenzo Librandi, Sep 12 2013 *)

Formula

A000040 \ {{2} U A165353}. - R. J. Mathar, Sep 21 2009

Extensions

Entries checked by R. J. Mathar, Sep 21 2009