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Search: id:A048611
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| A048611 |
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Find smallest pair (x,y) such that x^2-y^2 = 11...1 (n times) = (10^n-1)/9; sequence gives value of x. |
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+0
3
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| 1, 6, 20, 56, 156, 340, 2444, 4440, 167000, 55556, 267444, 333400, 132687920, 5555556, 10731400, 40938800, 2682647040, 333334000, 555555555555555556, 3334367856, 11034444280, 35595935980, 5555555555555555555556
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Least solutions for 'Difference between two squares is a repunit of length n'.
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REFERENCES
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David Wells, "Curious and Interesting Numbers", Revised Ed. 1997, Penguin Books, p. 119. ISBN 0-14-026149-4.
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LINKS
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H. Havermann, Repunit Square Differences (gives many more terms)
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EXAMPLE
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For n=2, 6^2-5^2=11.
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MATHEMATICA
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s = Flatten[Table[r = (10^i - 1)/9; d = Divisors[r]; p = d[[Length[d]/2]]; Solve[{x - y == p, x + y == r/p}, {y, x}], {i, 2, 56}]]; Prepend[Cases[s, Rule[x, n_] -> n], 1]
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CROSSREFS
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Cf. A048612, A000042, A002275.
Sequence in context: A109903 A014480 A048778 this_sequence A127982 A109164 A027984
Adjacent sequences: A048608 A048609 A048610 this_sequence A048612 A048613 A048614
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KEYWORD
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nonn,nice
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AUTHOR
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Felice Russo (felice.russo(AT)katamail.com)
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EXTENSIONS
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Corrected and extended by Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1999. More terms from Hans Havermann (pxp(AT)rogers.com), Jul 02 2000
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