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 A274027 #24 Jun 18 2025 11:32:57 %S A274027 1,162,324,3888,11664,18750,31250,32768,38416,40000,160000,167042, %T A274027 168750,253125,373248,607500,911250,1037232 %N A274027 Numbers k such that k^4 is the average of a positive cube and a positive fifth power. %C A274027 Numbers n such that 2*n^4 is of the form x^3 + y^5 where x and y are positive integers. %C A274027 Sequence is infinite because if m is a term, that is m^4 = (w^3 + z^5)/2 with w and z positive integers, then m*t^15 is also a term for every integer t>1. In fact: (m*t^15)^4 = ((w*t^20)^3 + (z*t^12)^5)/2. %e A274027 162 = 3*54 is a term because (3*54)^4 = ((18*54)^3 + 54^5)/2. %e A274027 38416 = 14^4 is a term because (14^4)^4 = ((3*14^5)^3 + (14^3)^5)/2. %o A274027 (PARI) isA100293(n) = for(y=1, sqrtnint(n-1, 5), if(ispower(n-y^5, 3), return(1))); 0; %o A274027 lista(nn) = for(n=1, nn, if(isA100293(2*n^4), print1(n, ", "))); %Y A274027 Cf. A000583, A100293. %K A274027 nonn,more %O A274027 1,2 %A A274027 _Altug Alkan_, Jun 07 2016 %E A274027 a(11)-a(18) from _Giovanni Resta_, Jun 07 2016