A344868 Primes p that are equal to (prime(k)+2*prime(k+1)+3*prime(k+2))/2 for some k.

17, 101, 191, 227, 293, 431, 461, 557, 571, 757, 821, 863, 1039, 1193, 1213, 1277, 1291, 1307, 1373, 1483, 1499, 1721, 1811, 2239, 2293, 2309, 2447, 2689, 3167, 3181, 3547, 3617, 3701, 3881, 4243, 4441, 4703, 4723, 4871, 5651, 6079, 6101, 6133, 6829, 6907, 6997, 7523, 7853, 7879, 7949

Offset: 1

Author

Zak Seidov, May 31 2021

Keywords

• nonn

Comments

Corresponding values of k: 2, 10, 17, 20, 24, 33, 35, 41, 42, 53, 57, 60, 68, 77, 78, 81, 82, 83, 87, 93, 94, 104, 109, 131, 134, 135, 140, 153, 176, 177, 193, 196, 201, 209, 222, 233, 246, 247, 256, 288, 306, 307, 308, 337, 341, 344, 367, 379, 380, 382, 393, 395.

Examples

			17 = (3 + 2*5 + 3*7)/2, 101 = (29 + 2*31 + 3*37)/2.
		

Links

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

Crossrefs

Cf. A034962.

Programs

Mathematica

s = {}; Do[If[PrimeQ[p = (Prime[k] + 2*Prime[k + 1] + 3*Prime[k + 2])/2], AppendTo[s, p]], {k, 400}]; s
Select[(#[[1]]+2#[[2]]+3#[[3]])/2&/@Partition[Prime[ Range[ 500]],3,1],PrimeQ] (* Harvey P. Dale, Jan 28 2022 *)

PARI

{p = 3; q = 5; r = 7; for (k = 1, 400, if (isprime (P = (p + 2*q + 3*r)/2), print1 (P ", ")); p = q; q = r; r = nextprime (r + 2))}