A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square.

1, 4, 9, 144, 441, 44944

Offset

1,2

Comments

Note that (1) implies that the product of the digits is a square.

Next term, if it exists, is > 90000000000. - Larry Reeves (larryr(AT)acm.org), May 11 2001

References

Amarnath Murthy, The Smarandache multiplicative square sequence is infinite, (to be published in Smarandache Notions Journal).

Amarnath Murthy, Infinitely many common members of the Smarandache additive as well as multiplicative square sequence, (to be published in Smarandache Notions Journal).

Links

Table of n, a(n) for n=1..6.

Felice Russo, A Set of New Smarandache Functions, Sequences and Conjectures in Number Theory, Lupton, AZ: American Research Press, 2000.

Example

For example, 44944 = 212^2, each digit is a square, sum of digits = 4+4+9+4+4 = 25 = 5^2.

Mathematica

For[n = 1, n < 100000, n++, a := DigitCount[n^2]; If[a[[2]] == 0, If[a[[3]] == 0, If[a[[5]] == 0, If[a[[6]] == 0, If[a[[7]] == 0, If[a[[8]] == 0, If[a[[10]] == 0, If[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]] == Floor[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]]], Print[n^2]]]]]]]]]] (* Stefan Steinerberger, Mar 15 2006 *)

Crossrefs

If zeros are allowed as digits, the result is A061270.

A subsequence of A006716.

Cf. A053057, A053059, A061267, A061268, A061269, A061270.

Sequence in context: A035127 A354078 A061267 * A061271 A084009 A306739

Adjacent sequences: A061266 A061267 A061268 * A061270 A061271 A061272

Keyword

nonn,base

Author

Amarnath Murthy, Apr 24 2001

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007

Status

approved