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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
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.
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
KEYWORD
nonn,nice
AUTHOR
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