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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 21 21:15 EDT 2019. Contains 327282 sequences. (Running on oeis4.)