A098142 Numbers n such that (p*(q-1)+(p-1)*q)/2 is prime, where p and q are consecutive odd primes, p<q and p_n is the n-th prime.

2, 3, 5, 9, 13, 15, 17, 26, 35, 43, 56, 60, 80, 81, 83, 86, 89, 101, 102, 104, 120, 140, 152, 157, 170, 178, 191, 201, 204, 215, 219, 223, 238, 252, 286, 293, 296, 324, 329, 350, 359, 373, 383, 392, 395, 398, 412, 416, 424, 444, 458, 468, 479, 487, 497, 503, 514

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, r = (p*(q - 1) + (p - 1)*q)/2; If[ PrimeQ[r], r, 0]]; Select[ Range[522], f[ # ] != 0 &]
Position[Partition[Prime[Range[600]], 2, 1], _?(PrimeQ[(#[[1]](#[[2]]-1)+(#[[1]]-1) #[[2]])/2]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Feb 23 2023 *)

Crossrefs

The generator of A099911.

Sequence in context: A366482 A087146 A033945 * A270812 A066821 A108568

Adjacent sequences: A098139 A098140 A098141 * A098143 A098144 A098145

Keyword

nonn

Author

Reinhard Zumkeller and Robert G. Wilson v, Nov 02 2004

Status

approved