A099911 Primes of the form (p*(q-1) + (p-1)*q)/2, where p and q are consecutive odd primes.

11, 29, 131, 641, 1721, 2441, 3539, 10301, 22349, 36671, 70481, 79241, 170957, 175979, 186191, 198461, 212981, 304127, 313031, 324329, 434939, 655289, 777041, 852827, 1031231, 1126781, 1339781, 1511669, 1571237, 1741079, 1875521, 2003591

Offset

1,1

Comments

Or, primes of the form prime(n)*prime(n+1)- (prime(n)+prime(n+1))/2.

Subsequence of A099909.

Links

Table of n, a(n) for n=1..32.

Example

p=A000040(5)=11, q=A000040(5+1)=13: (11*(13-1)+(11-1)*13)/2 = (132+130)/2 = 131 = A000040(32), therefore 131 is a term.

Mathematica

f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, r = (p*(q - 1) + (p - 1)*q)/2; If[ PrimeQ[r], r, 0]]; l = {}; Do[a = f[n]; If[a != 0, AppendTo[l, a]], {n, 300}]; l (* Robert G. Wilson v, Nov 02 2004 *)
Select[((#[[1]](#[[2]]-1))+((#[[1]]-1)#[[2]]))/2&/@Partition[ Prime[ Range[ 2, 300]], 2, 1], PrimeQ] (* Harvey P. Dale, Nov 28 2018 *)

Crossrefs

Cf. A098142.

Sequence in context: A179502 A053703 A216559 * A118638 A088460 A168171

Adjacent sequences: A099908 A099909 A099910 * A099912 A099913 A099914

Keyword

nonn

Author

Reinhard Zumkeller, Oct 29 2004

Extensions

More terms from Robert G. Wilson v, Nov 02 2004

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 21 2007

Status

approved