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A099911
Primes of the form (p*(q-1) + (p-1)*q)/2, where p and q are consecutive odd primes.
3
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.
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
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