A306103 - OEIS

%I #19 Jan 11 2020 03:06:12

%S 45,48,63,72,75,80,96,99,105,112,117,120,128,135,144,147,153,160,165,

%T 168,171,175,176,180,189,192,195,200,207,208,216,224,225,231,240,243,

%U 245,252,255,256,261,264,272,273,275,279,280,285,288,297,300

%N Numbers that are the difference of two positive squares in at least three ways.

%C Numbers n such that A100073(n) >= 3; see there for more information & formulas.

%H Metin Sariyar, <a href="/A306103/b306103.txt">Table of n, a(n) for n = 1..10000</a>

%H Geoffrey Campbell, <a href="https://www.linkedin.com/groups/4510047/4510047-6421706912643014658">Numbers that are the difference of two squares in two or more ways</a>, Number Theory Group on LinkedIn, July 8, 2018.

%F A306103 = { n = 2k+1 | A056924(n) > 2 } U { n = 4k | A056924(n/4) > 2 }.

%e 48 = 7^2 - 1^2 = 8^2 - 4^2 = 13^2 - 11^2.

%t Select[Range[300], Length[FindInstance[x^2 - y^2 == # && x>y>0, {x,y}, Integers, 3 ]] == 3 &] (* _Giovanni Resta_, Jul 10 2018 *)

%o (PARI) select( is(n)=A100073(n)>2, [1..300])

%Y Cf. A100073, A058957, A056924.

%Y Subsequence of A306102. Contains A306104 as a subsequence.

%K nonn

%O 1,1

%A Geoffrey B. Campbell and _M. F. Hasler_, Jul 10 2018