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A321350 Triangle read by rows: first row is 2; given row k, define the elements of row k+1 to be the (sorted) elements derived from row k by two recursion rules: (i.) if x is in row k, then (x+3)^2 is in row k+1; (ii.) if x^2 is in row k, then x is in row k+1.

%I A321350 #17 Dec 08 2018 17:49:31
%S A321350 2,25,5,784,28,64,619369,8,787,961,4489,383621674384,31,67,121,619372,
%T A321350 624100,929296,20178064,147165589059485451825769,11,790,964,1156,4492,
%U A321350 4900,15376,383621674387,383625390625,389504554609,863596631401,407154387856489,21657710603225344113280242498332241368243395984
%N A321350 Triangle read by rows: first row is 2; given row k, define the elements of row k+1 to be the (sorted) elements derived from row k by two recursion rules: (i.) if x is in row k, then (x+3)^2 is in row k+1; (ii.) if x^2 is in row k, then x is in row k+1.
%C A321350 A variant of A296142, a sequence inspired by problem A1 on the 2017 William Lowell Putnam Mathematical Competition.
%e A321350 First few rows are
%e A321350 2;
%e A321350 25;
%e A321350 5, 784;
%e A321350 28, 64, 619369;
%e A321350 8, 787, 961, 4489, 383621674384;
%e A321350 31, 67, 121, 619372, 624100, 929296, 20178064, 147165589059485451825769;
%e A321350 11, 790, 964, 1156, 4492, 4900, 15376, 383621674387, 383625390625, 389504554609, 863596631401, 407154387856489, 21657710603225344113280242498332241368243395984;
%Y A321350 Cf. A296142, A321351.
%K A321350 nonn,tabf
%O A321350 1,1
%A A321350 _Jeremy F. Alm_, Nov 06 2018