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 A050798 #20 Feb 16 2025 08:32:40
%S A050798 1,7,8,12,13,17,21,22,23,27,28,30,31,33,34,37,41,42,44,46,48,50,52,53,
%T A050798 55,58,60,62,63,64,67,75,76,77,78,80,81,86,87,88,89,91,92,96,97,100,
%U A050798 102,103,104,105,106,108,109,111,113,114,115,119,125,127,129,135,136
%N A050798 Numbers n such that m = n^2 + 1 is expressible as the sum of two nonzero squares in exactly two ways.
%C A050798 Of course m = n^2 + 1 is the sum of two squares, by definition. Here there should be just one other way to write m as a different sum of two squares.
%C A050798 Let p and q be primes of the form 1+4k. Then n^2+1 must be pq or 2pq. - _T. D. Noe_, May 27 2008
%H A050798 T. D. Noe, <a href="/A050798/b050798.txt">Table of n, a(n) for n=1..1000</a>
%H A050798 Eric Weisstein, <a href="https://mathworld.wolfram.com/SumofSquaresFunction.html">MathWorld: Sum of Squares Function</a>
%H A050798 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A050798 E.g., 111^2 + 1 = 21^2 + 109^2 only.
%t A050798 ok[1] = True; ok[n_] := Length[ {ToRules[ Reduce[ 1 < x <= y && n^2 + 1 == x^2 + y^2, {x, y}, Integers] ] } ] == 1; Select[ Range[136], ok] (* _Jean-François Alcover_, Feb 16 2012 *)
%Y A050798 Cf. A000161, A050797, A050796.
%K A050798 nonn,nice
%O A050798 1,2
%A A050798 _Patrick De Geest_, Sep 15 1999
%E A050798 Better definition from _T. D. Noe_, May 27 2008