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 A346115 #88 Nov 30 2021 03:03:35
%S A346115 5,65,1625,469625,642916625,15697403475,2474052064291275
%N A346115 Least number k such that k^2 can be expressed in exactly n ways as x^2 + y^4 with {x, y} >= 1.
%C A346115 a(5) <= 642916625. - _Hugo Pfoertner_, Jul 07 2021
%C A346115 From _Karl-Heinz Hofmann_, Sep 02 2021: (Start)
%C A346115 a(6) <= 15697403475.
%C A346115 2 * 10^10 < a(7) <= 2474052064291275.
%C A346115 These two conjectured values arise from the "green group". Up to term a(5) the least solutions are in the "blue group". Follow the links below to get more information about the different colored groups.
%C A346115 Terms cannot be a square (see the comment from Altug Alkan in A111925).
%C A346115 Terms must have at least one prime factor of the form p == 1 (mod 4), a Pythagorean prime (A002144).
%C A346115 If the terms additionally have prime factors of the form p == 3 (mod 4), which are in A002145, then they must appear in the prime divisor sets of x and y too. The special prime factor 2 has the same behavior, i.e., if the term is even, x and y must be even too. (End)
%H A346115 Karl-Heinz Hofmann, <a href="/A346110/a346110_1.pdf">All valid {z,x1,y1,x2,y2,x3,y3,x4,y4} sets up to 10^9 </a>
%H A346115 Karl-Heinz Hofmann, <a href="/A346110/a346110.gif">A 3D Animation of the 4 solutions and the least 5 solution up to 10^9 </a>
%e A346115 a(1)=A345645(1); a(2)=A345700(1); a(3)=A345968(1); a(4)=A346110(1).
%Y A346115 Cf. A000290, A000583, A111925.
%Y A346115 Cf. A271576 (1 or more solutions), A345645 (1 solution), A345700 (2 solutions), A345968 (3 solutions), A346110 (4 solutions), A348655 (5 solutions), A349324 (6 solutions).
%Y A346115 Cf. A002144 (p == 1 (mod 4)), A002145 (p == 3 (mod 4)).
%K A346115 nonn,hard,more
%O A346115 1,1
%A A346115 _Karl-Heinz Hofmann_, Jul 05 2021
%E A346115 a(5) confirmed by _Martin Ehrenstein_, Jul 09 2021
%E A346115 a(6) confirmed by _Karl-Heinz Hofmann_, Oct 15 2021
%E A346115 a(7) confirmed by _Jon E. Schoenfield_, Nov 15 2021