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 A274033 #23 Jun 18 2025 11:25:39 %S A274033 81250,1062882,11529602,12500000,170061120,200000000,2662400000, %T A274033 5897400777,7309688832,12814453125,34297420960,37019531250 %N A274033 Numbers k such that k = a^2 + b^4 and n^2 = c^3 + d^5 for some positive integers a, b, c, d. %C A274033 In other words, values of a^2 + b^4 such that (a^2 + b^4)^2 is of the form c^3 + d^5 where a, b, c, d > 0. %C A274033 81250 is the least number with this property. %C A274033 Sequence is infinite: If n = a^2 + b^4 and n^2 = c^3 + d^5, then n*k^60 = (a*k^30)^2 + (b*k^15)^4 and (n*k^60)^2 = (c*k^40)^3 + (d*k^24)^5. So if n is in this sequence, then n*k^60 is in this sequence for all nonzero values of k. %e A274033 81250 is a term because 81250 = 175^2 + 15^4 and 81250^2 = 1875^3 + 25^5. %Y A274033 Cf. A100293, A111925. %K A274033 nonn,more %O A274033 1,1 %A A274033 _Altug Alkan_, Jun 07 2016 %E A274033 a(2)-a(6) from _Giovanni Resta_, Jun 07 2016 %E A274033 a(7) from _Chai Wah Wu_, Jun 14 2016 %E A274033 a(8)-a(12) from _Chai Wah Wu_, Jul 07 2016