A100558 Primes of the form [prime(n)*prime(n+1)+p]/2 with increasing p.

11, 23, 47, 83, 131, 191, 263, 397, 563, 709, 953, 1091, 1289, 1531, 1867, 2129, 2389, 2729, 2963, 3259, 3659, 4099, 4787, 5387, 5693, 6101, 6473, 6803, 7829, 8999, 9697, 10247, 11117, 12041, 12703, 13669, 14549, 15439, 16573, 17321, 18461, 19661

Offset

1,1

Comments

Also primes equal to the arithmetic mean between product of two consecutive primes and prime p.

Links

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

Example

a(2)=11 because 11=(3*5+7)/2 and p is 7;
a(3)=23 because 23=(5*7+11)/2 and p is 11;
a(4)=47 because 47=(7*11+17)/2 and p is 17;
a(5)=83 because 83=(11*13+23)/2 and p is 23.

Mathematica

a[2] = 11; a[n_] := a[n] = Block[{k = PrimePi[2a[n - 1] - Prime[n - 1]Prime[n]] + 1, q = Prime[n]Prime[n + 1]}, While[p = Prime[k]; !PrimeQ[(q + p)/2], k++ ]; (q + p)/2]; Table[ a[n], {n, 2, 43}] (* Robert G. Wilson v, Nov 29 2004 *)

Crossrefs

Sequence in context: A145994 A217047 A139834 * A126199 A096342 A066179

Adjacent sequences: A100555 A100556 A100557 * A100559 A100560 A100561

Keyword

nonn

Author

Giovanni Teofilatto, Nov 28 2004

Extensions

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

Status

approved