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A192612
Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 and 2 are in S.
3
1, 2, 3, 11, 17, 19, 139, 251, 307, 379, 587
OFFSET
1,2
COMMENTS
See the discussions at A192476 and A192580. The start-set for A192612 is {1,2}. For results using start-sets {1}, and {1,2,4}, see A192598 and A192613.
MATHEMATICA
start = {1, 2}; primes = Table[Prime[n], {n, 1, 20000}];
f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 2 y^2]
b[x_] :=
Block[{w = x},
Select[Union[
Flatten[AppendTo[w,
Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
Length[w]}]]]], # < 30000 &]];
t = FixedPoint[b, start] (* A192612 *)
CROSSREFS
KEYWORD
nonn,full,fini
AUTHOR
Clark Kimberling, Jul 05 2011
STATUS
approved