A257417 - OEIS

A257417

Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.

%I #20 Apr 24 2023 12:13:15

%S 960,1344,1728,2112,2240,2496,2592,2835,3240,3264,3520,3648,4160,4416,

%T 4455,4536,4928,5265,5440,5568,5824,5952,6080,6144,6237,6885,7104,

%U 7128,7360,7371,7616,7695,7872,8000,8256,8424,8512,9024,9152,9280,9315,9639,9920

%N Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.

%H David A. Corneth, <a href="/A257417/b257417.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Colin Barker)

%e 960 is in the sequence because there are 10 solutions to x^2 - y^2 = 960, namely (x,y) = (31,1), (32,8), (34,14), (38,22), (46,34), (53,43), (64,56), (83,77), (122,118), (241,239).

%t nn = 10000;

%t t = Table[0, {nn}];

%t Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];

%t Position[t, 10] // Flatten (* _Jean-François Alcover_, Jun 18 2020, after _T. D. Noe_ in A034178 *)

%o (PARI) is_A257417(n)={A034178(n)==10} \\ _M. F. Hasler_, Apr 22 2015

%Y Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257415, A257416.

%Y Cf. A034178.

%K nonn

%O 1,1

%A _Colin Barker_, Apr 22 2015