A100557 Smallest prime of the form (prime(n)*prime(n+1)+q)/2 for some integer n and some prime q.

11, 19, 41, 73, 113, 163, 227, 337, 461, 577, 761, 883, 1013, 1249, 1567, 1801, 2053, 2381, 2593, 2887, 3299, 3697, 4337, 4919, 5231, 5519, 5843, 6173, 7177, 8363, 9007, 9533, 10357, 11251, 11863, 12799, 13613, 14447, 15493, 16223, 17291, 18433, 19013

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Example

a(2) = 19 because 19 = (5*7 + 3)/2;
a(3) = 41 because 41 = (7*11 + 5)/2;
a(4) = 83 because 73 = (11*13 + 3)/2.

Mathematica

f[n_] := Block[{k = 2, q = Prime[n]Prime[n + 1]}, While[p = Prime[k]; !PrimeQ[(q + p)/2], k++ ]; (q + p)/2]; Table[ f[n], {n, 2, 44}] (* Robert G. Wilson v, Nov 29 2004 *)

Crossrefs

Sequence in context: A140506 A259190 A165944 * A066591 A061246 A353102

Adjacent sequences: A100554 A100555 A100556 * A100558 A100559 A100560

Keyword

nonn,easy

Author

Giovanni Teofilatto, Nov 28 2004

Extensions

Edited, corrected and extended by Robert G. Wilson v, Nov 29 2004

Status

approved