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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
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
Sequence in context: A260777 A014480 A048778 * A292480 A200528 A127982
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

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)