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 A355769 #20 Sep 09 2022 04:04:48 %S A355769 17,25,40,52,72,73,89,97,100,116,136,145,148,169,180,193,225,232,233, %T A355769 241,244,260,288,289,292,305,313,337,369,388,400,404,409,424,449,457, %U A355769 481,520,521,544,548,577,584,585,592,612,625,628,640,656,673,676,697,724 %N A355769 Numbers k such that both k and k+1 can be written as the sum of two nonzero squares. %C A355769 The numbers in the sequence are useful in solving various second-degree Diophantine equations. %C A355769 The identity (3n-12)^2 + (4n-12)^2 + 1 = (3n-8)^2 + (4n-15)^2 proves that there are infinitely many such numbers in this sequence. %e A355769 17 is a term since 17 = 4^2 + 1^2 and 17 + 1 = 18 = 3^2 + 3^2. %e A355769 169 is a term since 169 = 5^2 + 12^2 and 169 + 1 = 170 = 1^2 + 13^2. %o A355769 (PARI) is1(n)= for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)); \\ A000404 %o A355769 isok(k) = is1(k) && is1(k+1); \\ _Michel Marcus_, Jul 18 2022 %Y A355769 Cf. A000290, A000404, A000415. %K A355769 nonn %O A355769 1,1 %A A355769 _Angad Singh_, Jul 16 2022