A164580 Primes of the form p^2 + (p + 1)/2 where p is also prime.

11, 53, 127, 541, 977, 1871, 3511, 4523, 5077, 11503, 16193, 19391, 22877, 57241, 63127, 80231, 129061, 134873, 143831, 229681, 241327, 344863, 359101, 398477, 418933, 434611, 619763, 658127, 745201, 845021, 966781, 982577, 1063477, 1130501, 1371827

Offset

1,1

Links

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

Formula

a(n) = (A154427(n))^2 + ( A154427(n)+1)/2.

Example

For p=3, p^2+(p+1)/2=11, prime, which adds 11 to the sequence. For p=7, p^2+(p+1)/2=53, which adds 53 to the sequence.

Mathematica

Select[Table[p^2 + (p + 1)/2, {p, Prime[Range[200]]}], PrimeQ] (* Vincenzo Librandi, Oct 12 2012 *)

Prog

(Magma) [a: p in PrimesInInterval(3, 1200) | IsPrime(a) where a is p^2 + (p+1) div 2 ]; // Vincenzo Librandi, Oct 12 2012

Crossrefs

Cf. A154427.

Sequence in context: A086715 A178453 A225582 * A141893 A093198 A207361

Adjacent sequences: A164577 A164578 A164579 * A164581 A164582 A164583

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 17 2009

Extensions

Edited and extended by R. J. Mathar, Aug 26 2009

Status

approved