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Search: id:A048612
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| A048612 |
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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 y. |
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+0
3
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| 0, 5, 17, 45, 115, 67, 2205, 2933, 166667, 44445, 245795, 6667, 132683733, 4444445, 2012917, 23767083, 2680575317, 666667, 555555555555555555, 83053525, 3263104267, 12488376483, 5555555555555555555555, 66666667, 2952525627555
(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[y, n_] -> n], 0]
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CROSSREFS
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Cf. A048611, A000042, A002275.
Sequence in context: A163424 A099451 A133252 this_sequence A147050 A147397 A147193
Adjacent sequences: A048609 A048610 A048611 this_sequence A048613 A048614 A048615
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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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