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

1, 4, 9, 25, 36, 49, 169, 256, 289, 576, 676, 1849, 3844, 3969, 5776, 6889, 26896, 27889, 55696, 69696, 97969, 339889, 376996, 499849, 678976, 698896, 779689, 2679769, 2768896, 2778889, 4695889, 4999696, 9696996, 26697889, 28879876, 36759969, 37994896

Offset

1,2

Comments

The triangular numbers of this form are at A246753.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..116

Example

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.
From Wolfdieter Lang, Oct 31 2014: (Start)
A053667 is sieved (from the left to the right):
1, 2, 3, 4,  5,  6,  7,  8, 9, 10, 11, 12, 13, 14, ...
1, 4, 9, 6, 10, 18, 36, 24, 8,  0,  2, 16, 54, 54, ...
1, 4, 9, x, 10, 18, 36,  x, x,  x,  x,  x, 54,  x, ...
and the related leftover squares are
1, 4, 9,    25  36, 49,                    169,    ...
(End)
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Mathematica

A248648 = {}; k = 0; Do[s = Apply[Times, IntegerDigits[n^2]]; If[s > k, k = s; AppendTo[A248648, n^2]], {n, 1, 10^4}]; A248648

Prog

(PARI)
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

Crossrefs

Cf. A000290, A230041, A246569, A246753, A053667.

Sequence in context: A111245 A366243 A062503 * A063577 A087058 A046659

Adjacent sequences: A248645 A248646 A248647 * A248649 A248650 A248651

Keyword

nonn,base,easy

Author

K. D. Bajpai, Oct 10 2014

Extensions

Edited, Name specified, example reformulated, A053667 and 'easy' added. - Wolfdieter Lang, Oct 31 2014

Status

approved