%I
%S 1,2,3,4,8,9,16,26,27,34,50,57,70,74,75,88,104,111,112,116,153,178,
%T 188,207,238,242,243,268,278,285,286,308,327,358,362,381,394,416,417,
%U 424,452,453,466,470,501,502,506,519,538,566,567,574,590,597,610,614,615
%N 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.
%C Inspired by A073627, A073628. Primes generated in the sequence are in A075551. Primes generated in A073628 are in A075552.
%H Harvey P. Dale, <a href="/A074311/b074311.txt">Table of n, a(n) for n = 1..1000</a>
%e a(5) = 8 because 1/3(a(3) + a(4) + a(5)) is a prime.
%t 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 *)
%Y Cf. A073627, A073628, A075551, A075552.
%K nonn
%O 1,2
%A _Zak Seidov_, Sep 23 2002
