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A100558 Primes of the form [prime(n)*prime(n+1)+p]/2 with increasing p. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)