A058957 Numbers having at least two representations as b^2 - c^2 with b > c >= 0.

9, 15, 16, 21, 24, 25, 27, 32, 33, 35, 36, 39, 40, 45, 48, 49, 51, 55, 56, 57, 60, 63, 64, 65, 69, 72, 75, 77, 80, 81, 84, 85, 87, 88, 91, 93, 95, 96, 99, 100, 104, 105, 108, 111, 112, 115, 117, 119, 120, 121, 123, 125, 128, 129, 132, 133, 135, 136, 140, 141, 143

Offset: 1

Author

Henry Bottomley, Jan 13 2001

Keywords

• nonn

Comments

This is the union of the squares > 4 and A306102: numbers that are the difference of two positive squares in at least two ways (where c=0 is excluded). - M. F. Hasler, Jul 12 2018

Examples

			9 is in the sequence since 9 = 3^2 - 0^2 = 5^2 - 4^2;
45 is in the sequence since 45 = 7^2 - 2^2 = 9^3 - 6^2 = 23^2 - 22^2.
		

Crossrefs

Cf. A034178, A016825.

Cf. A306102 (subsequence and variant using c > 0).

Programs

Mathematica

Select[Range@143, Length@ FindInstance[x^2 - y^2 == # && x>y>= 0, {x, y}, Integers, 2] == 2 &] (* Giovanni Resta, Jul 10 2018 *)

PARI

select( is(n)=fordiv(n, d, d^2 > n && return; (n-d^2)%(2*d) || c++<2 || return(1)), [1..200]) \\ M. F. Hasler, Jul 10 2018

Formula

A058957 = { n | A034178(n) >= 2 }. - M. F. Hasler, Jul 10 2018

Extensions

Name edited by M. F. Hasler, Jul 10 2018