A118941 Primes p such that (p^2-5)/4 is prime.

5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 53, 61, 71, 79, 83, 89, 97, 101, 107, 109, 113, 131, 137, 167, 173, 179, 193, 229, 241, 251, 263, 269, 277, 281, 283, 307, 311, 317, 349, 353, 373, 383, 419, 431, 439, 461, 463, 467, 563, 571, 577, 593, 607, 613, 619, 647

Offset

1,1

Comments

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 4 divides q^2-5. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118940 and A118942.

Links

Table of n, a(n) for n=1..56.

Mathematica

Select[Prime[Range[200]], PrimeQ[(#^2-5)/4]&]

Crossrefs

Sequence in context: A216523 A230227 A101635 * A096547 A216524 A128824

Adjacent sequences: A118938 A118939 A118940 * A118942 A118943 A118944

Keyword

nonn

Author

T. D. Noe, May 06 2006

Status

approved