A074311 a(1) = 1; a(2) = 2; a(n) = smallest number greater than the previous term such that the average of three successive terms is a prime.

1, 2, 3, 4, 8, 9, 16, 26, 27, 34, 50, 57, 70, 74, 75, 88, 104, 111, 112, 116, 153, 178, 188, 207, 238, 242, 243, 268, 278, 285, 286, 308, 327, 358, 362, 381, 394, 416, 417, 424, 452, 453, 466, 470, 501, 502, 506, 519, 538, 566, 567, 574, 590, 597, 610, 614, 615

Offset

1,2

Comments

Inspired by A073627, A073628. Primes generated in the sequence are in A075551. Primes generated in A073628 are in A075552.

Links

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

Example

a(5) = 8 because 1/3(a(3) + a(4) + a(5)) is a prime.

Mathematica

sngpt[{a_, b_}]:=Module[{k=b+1}, While[CompositeQ[Mean[{a, b, k}]], k++]; {b, k}]; NestList[sngpt, {1, 2}, 60][[All, 1]] (* Harvey P. Dale, May 29 2019 *)

Crossrefs

Cf. A073627, A073628, A075551, A075552.

Sequence in context: A045583 A045608 A068317 * A076382 A006899 A256179

Adjacent sequences: A074308 A074309 A074310 * A074312 A074313 A074314

Keyword

nonn

Author

Zak Seidov, Sep 23 2002

Status

approved