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 A368418 #25 Jan 29 2024 19:22:18 %S A368418 10,76,100,980,1000,8824,10000,76249,87551,98020,100000,753424,766424, %T A368418 999800,1000000,7209049,7241380,8220640,8463640,9801980,9879740, %U A368418 9990280,10000000,77053825,78173720,80404255,83754376,84711551,86600176,90880001,93094625,93728480 %N A368418 Numbers X such that X^2 + Y^2 = 10^(2*k) + 1, with X > Y > 0 and k is the decimal digit length of X-1. %C A368418 The values X and Y are used in finding A368416. %C A368418 The number of terms for a given k is 2^(f-1), where f = A119704(2*k) is the number of prime factors of 10^(2*k) + 1. %D A368418 Frits Beukers, "Getallen - Een inleiding" (In Dutch), Epsilon Uitgaven, Amsterdam (2015). %H A368418 A.H.M. Smeets, <a href="/A368418/b368418.txt">Table of n, a(n) for n = 1..67</a> %H A368418 T. Granlund, <a href="http://gmplib.org/~tege/fac10p.txt">Factors of 10^n + 1</a>. %H A368418 Alf van der Poorten, <a href="https://link.springer.com/chapter/10.1007/978-3-0348-8295-8_12">The Hermite-Serret Algorithm and 12^2 + 33^2</a>. In: Lam, KY., Shparlinski, I., Wang, H., Xing, C. (eds) Cryptography and Computational Number Theory. Progress in Computer Science and Applied Logic, vol 20. Birkhäuser, Basel. %e A368418 10 is a term since X = 10, Y = 1, k = 1 and 10^2 + 1^2 = 101. %e A368418 76 is a term since X = 76, Y = 65, k = 2 and 76^2 + 65^2 = 10001. %e A368418 980 is a term since X = 980, Y = 199, k = 3 and 980^2 + 199^2 = 1000001. %Y A368418 Cf. A098608, A119704, A368416. %K A368418 nonn,base %O A368418 1,1 %A A368418 _A.H.M. Smeets_, Dec 24 2023