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A253237 Conjectured largest perfect power k such that k+n is also a perfect power, or 0 if no such k exists. 0
8, 25, 125, 121, 27, 0, 32761, 97336, 64000, 2187, 3364, 2197, 4900, 0, 1295029, 128, 143384152904, 343, 503284356, 196, 100, 2187, 2025, 542939080312, 144, 6436343, 216, 131044, 196, 6859, 225, 7744, 256, 0, 1296, 1728, 14348907, 1331, 10609, 2704, 400, 0, 441, 125, 9216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Only a(1) is proven, all other terms (even including a(2)) are only conjectured.

These terms are searched up to 10^18, and no terms are greater than 10^12.

a(n) = A103953(n) for n in A076438.

See A076427 for further information. - M. F. Hasler, Apr 09 2015

LINKS

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Pillai's Conjecture

Wikipedia, Catalan's conjecture

Wikipedia, Hall's conjecture

FORMULA

a(A074981(n)) = 0.

CROSSREFS

Cf. A001597, A074981, A076427, A076438, A103953.

Sequence in context: A181207 A068315 A069586 * A275151 A302617 A042189

Adjacent sequences:  A253234 A253235 A253236 * A253238 A253239 A253240

KEYWORD

nonn,hard,nice

AUTHOR

Eric Chen, Apr 04 2015

STATUS

approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)