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
KEYWORD
nonn
AUTHOR
Zak Seidov, May 31 2021
STATUS
approved