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Search: id:A061844
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| A061844 |
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Squares which remain squares if you decrease every digit by 1. |
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+0
2
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| 1, 36, 3136, 24336, 5973136, 71526293136, 318723477136, 264779654424693136, 24987377153764853136, 31872399155963477136, 58396845218255516736, 517177921565478376336, 252815272791521979771662766736
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The terms may be calculated efficiently by solving x^2 - y^2 = 111...1; this is done by factoring 111..1 = (x + y)(x - y).
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EXAMPLE
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E.g. 13225 = 115^2 and 24336 = 156^2.
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MATHEMATICA
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For[digits = 1, digits <= 30, digits++, n = (10^digits - 1)/9; divList = Select[Divisors[n], (#1 >= Sqrt[n])&];
For[j = 1, j <= Length[divList], j++, x = (divList[[j]] + n/divList[[j]])/2; y = (divList[[j]] - n/divList[[j]])/2;
dx = IntegerDigits[x^2]; dy = IntegerDigits[y^2];
If[(Length[dx] == digits) && (Length[dy] == digits) && (Select[dx, (#1 == 0)&] == {}), Print[x^2]]]]
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CROSSREFS
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Sequence in context: A120466 A159728 A004706 this_sequence A036510 A034983 A072377
Adjacent sequences: A061841 A061842 A061843 this_sequence A061845 A061846 A061847
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KEYWORD
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base,nonn,nice
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AUTHOR
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Erich Friedman (efriedma(AT)stetson.edu), Jun 23 2001
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EXTENSIONS
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More terms and program from Jonathan Cross (jcross(AT)wcox.com), Oct 08 2001
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