This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080262 #23 Feb 16 2025 08:32:48 %S A080262 3,5,7,8,9,10,15,17,24,26,28,31,33,35,37,48,50,63,65,80,82,99,101,120, %T A080262 122,124,126,127,129,143,145,168,170,195,197,215,217,224,226,242,244, %U A080262 255,257,288,290,323,325,342,344,360,362,399,401,440,442,483,485,511 %N A080262 Cunningham numbers: of the form a^b +- 1, where a, b >= 2. %C A080262 Named after the British mathematician Allan Joseph Champneys Cunningham (1842-1928). - _Amiram Eldar_, Apr 02 2022 %H A080262 Amiram Eldar, <a href="/A080262/b080262.txt">Table of n, a(n) for n = 1..10000</a> %H A080262 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CunninghamNumber.html">Cunningham Number</a>. %H A080262 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cunningham_number">Cunningham number</a>. %F A080262 a(2n) = A001597(n+2)-1, a(2n+1) = A001597(n+2)+1 for n >= 5, if (25,27) is the only pair of perfect powers that differ by 2. (Note that it is known as Mihăilescu's theorem (formerly called Catalan's conjecture) that (8,9) is the only pair of perfect powers who differ by 1.) - _Jianing Song_, Oct 15 2022 %e A080262 26 = 3^3 - 1, 126 = 5^3 + 1 are Cunningham numbers. %t A080262 powerQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[2^9], powerQ[# - 1] || powerQ[# + 1] &] (* _Amiram Eldar_, Jul 27 2019 *) %Y A080262 Cf. A001597 (the perfect powers). %K A080262 nonn %O A080262 1,1 %A A080262 _David W. Wilson_, Feb 11 2003