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A061269
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Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square.
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5
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OFFSET
| 1,2
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COMMENTS
| Note that (1) implies that the product of the digits is a square.
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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).
Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000
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LINKS
| M. L. Perez et al., eds., Smarandache Notions Journal
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EXAMPLE
| For example, 44944= 212^2, each digit is a square, sum of digits = 4+4+9+4+4 = 25 = 5^2.
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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 (stefan.steinerberger(AT)gmail.com), Mar 15 2006
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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 A061267 * A061271 A084009 A029738 A067072
Adjacent sequences: A061266 A061267 A061268 * A061270 A061271 A061272
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KEYWORD
| nonn,base
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2001
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EXTENSIONS
| Next term, if it exists, is > 90000000000 - Larry Reeves (larryr(AT)acm.org), May 11 2001
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 05 2007
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