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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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))}

Crossrefs

Cf. A034962.

Sequence in context: A139497 A139913 A255417 * A186258 A175518 A215234

Adjacent sequences: A344865 A344866 A344867 * A344869 A344870 A344871

Keyword

nonn

Author

Zak Seidov, May 31 2021

Status

approved