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 A138760 #8 Feb 16 2025 08:33:08 %S A138760 5491,10982,16473,21964,27455,32946,38437,43928,49419,51361,54910, %T A138760 60401,65892,71383,76874,82365,87856,93347,98838,102722,104329,109820, %U A138760 115311,120802,126293,131784,137275,142766,148257,153748,154083,159239,164730 %N A138760 Numbers n such that n^4 is a sum of 4th powers of four nonzero integers whose sum is n. %C A138760 Any multiple of a member is also a member. A member that is not a multiple of another member is called primitive. Using elliptic curves, Jacobi and Madden prove that there are infinitely many primitive members. According to them, the only primitive members less than 222,000 are 5491 (due to Brudno) and 51361 (due to Wroblewski). %H A138760 Simcha Brudno, <a href="http://dx.doi.org/10.1017/S0305004100038470">A further example of A^4 + B^4 + C^4 + D^4 = E^4</a>, Proc. Camb. Phil. Soc. 60 (1964) 1027-1028. %H A138760 Noam Elkies, <a href="http://dx.doi.org/10.1090/S0025-5718-1988-0930224-9">On A^4 + B^4 + C^4 = D^4</a>, Math. Comp. 51 (1988) 825-835. %H A138760 Lee W. Jacobi and Daniel J. Madden, <a href="http://www.jstor.org/stable/27642446">On a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4</a>, Amer. Math. Monthly 115 (2008) 220-236. %H A138760 Lee W. Jacobi and Daniel J. Madden, <a href="http://www.maa.org/pubs/monthly_mar08_toc.html">On a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4</a> %H A138760 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/DiophantineEquation4thPowers.html">Diophantine equation - 4th powers</a> %H A138760 Jaroslaw Wroblewski, <a href="http://www.math.uni.wroc.pl/~jwr/eslp/414.txt">Exhaustive list of 1009 solutions to (4,1,4) below 222,000</a> %F A138760 n^4 = a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4 with abcd =/= 0. %e A138760 5491^4 = 5400^4 + (-2634)^4 + 1770^4 + 955^4 and 5491 = 5400 - 2634 + 1770 + 955, so 5491 is a member (Brudno). %e A138760 51361^4 = 48150^4 + (-31764)^4 + 27385^4 + 7590^4 and 51361 = 48150 - 31764 + 27385 + 7590, so 51361 is a member (Wroblewski). %e A138760 1347505009^4 = 1338058950^4 + (-89913570)^4 + 504106884^4 + (-404747255)^4, and 1347505009 = 1338058950 - 89913570 + 504106884 - 404747255, so 1347505009 is a member (Jacobi-Madden). %Y A138760 Cf. A003294, A003828, A096739. %K A138760 nonn %O A138760 1,1 %A A138760 _Jonathan Sondow_, Mar 28 2008