

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



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.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



