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A248648 The squares related to the strictly increasing subsequence of A053667(n), n >= 1.

%I A248648 #12 Jan 15 2018 15:31:27
%S A248648 1,4,9,25,36,49,169,256,289,576,676,1849,3844,3969,5776,6889,26896,
%T A248648 27889,55696,69696,97969,339889,376996,499849,678976,698896,779689,
%U A248648 2679769,2768896,2778889,4695889,4999696,9696996,26697889,28879876,36759969,37994896
%N A248648 The squares related to the strictly increasing subsequence of A053667(n), n >= 1.
%C A248648 The triangular numbers of this form are at A246753.
%H A248648 K. D. Bajpai, <a href="/A248648/b248648.txt">Table of n, a(n) for n = 1..116</a>
%e A248648 5 * 5 = 25 is a square and the product of its digits = 2 * 5 = 10. Because a(3) = 9, and 4 * 4 = 16 has product of digits 6 < 9, a(4) = 25 because 10 > 9. The next entry a(5) comes from 6 * 6 = 36 with product of digits 18 > 10.
%e A248648 From _Wolfdieter Lang_, Oct 31 2014: (Start)
%e A248648 A053667 is sieved (from the left to the right):
%e A248648 1, 2, 3, 4,  5,  6,  7,  8, 9, 10, 11, 12, 13, 14, ...
%e A248648 1, 4, 9, 6, 10, 18, 36, 24, 8,  0,  2, 16, 54, 54, ...
%e A248648 1, 4, 9, x, 10, 18, 36,  x, x,  x,  x,  x, 54,  x, ...
%e A248648 and the related leftover squares are
%e A248648 1, 4, 9,    25  36, 49,                    169,    ...
%e A248648 (End)
%e A248648 -------------------------------------------------------
%t A248648 A248648 = {}; k = 0; Do[s = Apply[Times, IntegerDigits[n^2]];If[s > k, k = s; AppendTo[A248648, n^2]], {n, 1, 10^4}]; A248648
%o A248648 (PARI)
%o A248648 product=0;for(n=1,10^5,d=digits(n^2);p=prod(i=1,#d,d[i]);while(p>product,print1(n^2,", ");product=p)) \\ _Derek Orr_, Oct 11 2014
%Y A248648 Cf. A000290, A230041, A246569, A246753, A053667.
%K A248648 nonn,base,easy
%O A248648 1,2
%A A248648 _K. D. Bajpai_, Oct 10 2014
%E A248648 Edited, Name specified, example reformulated, A053667 and 'easy' added. - _Wolfdieter Lang_, Oct 31 2014