A056203 Triangle of numbers related to congruum problem: T(n,k)=n^2+2nk-k^2 with n>k>0, starting at T(2,1)=7.

7, 14, 17, 23, 28, 31, 34, 41, 46, 49, 47, 56, 63, 68, 71, 62, 73, 82, 89, 94, 97, 79, 92, 103, 112, 119, 124, 127, 98, 113, 126, 137, 146, 153, 158, 161, 119, 136, 151, 164, 175, 184, 191, 196, 199, 142, 161, 178, 193, 206, 217, 226, 233, 238, 241, 167, 188

Offset

1,1

Comments

The congruum problem is to find h (A057103) such that there are integers x (A055096), y (A057105) and z (A056203) with h=x^2-y^2=z^2-x^2.

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Links

Table of n, a(n) for n=1..57.

Eric Weisstein's World of Mathematics, Congruum Problem.

Formula

a(n) = sqrt(A057103(n)+A055096(n)^2) = sqrt(2*A057103(n)+A057105(n)^2).

Example

a(1) = T(2,1) = 2^2+2*2*1-1 = 7.

Crossrefs

Cf. A057102.

Sequence in context: A254064 A257224 A092433 * A178732 A025021 A326767

Adjacent sequences: A056200 A056201 A056202 * A056204 A056205 A056206

Keyword

nonn,tabl

Author

Henry Bottomley, Aug 02 2000

Status

approved