A253237 Conjectured largest perfect power k such that k+n is also a perfect power, or 0 if no such k exists.

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

Offset: 1

Author

Eric Chen, Apr 04 2015

Keywords

• nonn
• hard
• nice

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

• Eric Weisstein's World of Mathematics, Pillai's Conjecture.
• Wikipedia, Catalan's conjecture.
• Wikipedia, Hall's conjecture.

Crossrefs

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

Formula

a(A074981(n)) = 0.