The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #34 Sep 17 2023 21:36:33
%S 8,25,125,121,27,0,32761,97336,64000,2187,3364,2197,4900,0,1295029,
%T 128,143384152904,343,503284356,196,100,2187,2025,542939080312,144,
%U 6436343,216,131044,196,6859,225,7744,256,0,1296,1728,14348907,1331,10609,2704,400,0,441,125,9216
%N Conjectured largest perfect power k such that k+n is also a perfect power, or 0 if no such k exists.
%C Only a(1) is proven, all other terms (even including a(2)) are only conjectured.
%C These terms are searched up to 10^18, and no terms are greater than 10^12.
%C a(n) = A103953(n) for n in A076438.
%C See A076427 for further information. - _M. F. Hasler_, Apr 09 2015
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PillaisConjecture.html">Pillai's Conjecture</a>.
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Catalan%27s_conjecture">Catalan's conjecture</a>.
%H Wikipedia, <a href="https://www.wikipedia.org/wiki/Hall%27s_conjecture">Hall's conjecture</a>.
%F a(A074981(n)) = 0.
%Y Cf. A001597, A074981, A076427, A076438, A103953.
%K nonn,hard,nice
%O 1,1
%A _Eric Chen_, Apr 04 2015