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 A048611 Find smallest pair (x,y) such that x^2 - y^2 = 11...1 (n times) = (10^n-1)/9; sequence gives value of x. 3
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 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 Table of n, a(n) for n=1..23. H. Havermann, Repunit Square Differences (gives many more terms) FORMULA a(n) = (A033677((10^n-1)/9)+A033676((10^n-1)/9))/2. - Chai Wah Wu, Apr 05 2021 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[x, n_] -> n], 1] PROG (Python) from sympy import divisors def A048611(n): d = divisors((10**n-1)//9) l = len(d) return (d[l//2]+d[(l-1)//2])//2 # Chai Wah Wu, Apr 05 2021 CROSSREFS Cf. A048612, A000042, A002275, A033676, A033677. Sequence in context: A260777 A014480 A048778 * A292480 A200528 A127982 Adjacent sequences: A048608 A048609 A048610 * A048612 A048613 A048614 KEYWORD nonn,nice AUTHOR Felice Russo EXTENSIONS Corrected and extended by Patrick De Geest, Jun 15 1999 More terms from Hans Havermann, Jul 02 2000 Offset corrected by Chai Wah Wu, Apr 05 2021 STATUS approved

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Last modified June 6 20:02 EDT 2023. Contains 363151 sequences. (Running on oeis4.)