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A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square. 5
1, 4, 9, 144, 441, 44944 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A035127 A354078 A061267 * A061271 A084009 A306739
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

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Last modified April 23 16:40 EDT 2024. Contains 371916 sequences. (Running on oeis4.)