

A061269


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


5




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: A227744 A035127 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



