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 A048612 Find smallest pair (x,y) such that x^2-y^2 = 11...1 (n times) = (10^n-1)/9; sequence gives value of y. 3
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Least solutions for 'Difference between two squares is a repunit of length n'. REFERENCES David Wells, "Curious and Interesting Numbers", Revised Ed. 1997, Penguin Books, p. 119. ISBN 0-14-026149-4. LINKS H. Havermann, Repunit Square Differences (gives many more terms) EXAMPLE For n=2, 6^2 - 5^2 = 11. MATHEMATICA 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] Join[{0}, Table[y/.Solve[{x>0, y>0, x^2-y^2==FromDigits[PadRight[{}, n, 1]]}, {x, y}, Integers][[1]], {n, 2, 30}]](* Harvey P. Dale, Jun 12 2018 *) CROSSREFS Cf. A048611, A000042, A002275. Sequence in context: A299335 A247618 A269962 * A320554 A218135 A271122 Adjacent sequences:  A048609 A048610 A048611 * A048613 A048614 A048615 KEYWORD nonn,nice AUTHOR EXTENSIONS Corrected and extended by Patrick De Geest, Jun 15 1999 More terms from Hans Havermann, Jul 02 2000 STATUS approved

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Last modified September 27 13:13 EDT 2020. Contains 337380 sequences. (Running on oeis4.)