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 A098122 #11 Feb 16 2025 08:32:54 %S A098122 0,1,2,1,4,3,2,11,24,7,38,41,44,117,278,29,336,527,718,1199,3116,237, %T A098122 2642,6469,10296,11753,33802,8839,16124,76443,136762,108691,354144, %U A098122 164833,24478,873121,1721764,922077,3565918,2521451,1476984,9653287 %N A098122 Let (A,B)=(a(2*n),a(2*n+1)), then (A,B) is (even,odd), gcd(A,B)=1 and A^2 + B^2 = 5^n. Note: a(0)=0. %C A098122 (a(4*n),a(4*n+1)) are legs of the unique Pythagorean right triangle with hypotenuse 5^n and relatively prime legs. %D A098122 Jacobi, C. G. J. (1829) Fundamenta Nova Theoriae Functionum Ellipticarum, Regiomonti, Sumptibus fratrum Borntraeger; reprinted in Jacobi, C. G. J. (1881-1891) Gesammelte Werke (Reimer, Berlin), Vol. 1, pp. 49-239 [reprinted (1969) by Chelsea, New York; now distributed by Am. Mathematical Soc., Providence, RI]. %H A098122 Elias M. Stein and Rami Shakarchi, <a href="http://pup.princeton.edu/chapters/s10_7563.pdf">Complex Analysis</a>, Ch. 10. %H A098122 XIAO Gang, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two Squares (a section of WWW Interactive Multipurpose Server)</a> %H A098122 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofSquaresFunction.html">Sum of Squares Function</a> %e A098122 (a(2*3),a(2*3+1)) = (2,11) because (2,11) are (even,odd), relatively prime and 2^2 + 11^2 = 5^3. There is just one such pair. %Y A098122 Cf. A006495, A006496 (the odd and even numbers separately). %K A098122 nonn %O A098122 0,3 %A A098122 _James R. Buddenhagen_, Sep 24 2004