A117475 The values of c in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c) = 1.

37, 65, 205, 373, 1193, 2173, 6953, 12665, 40525, 73817, 236197, 430237, 1376657, 2507605, 8023745, 14615393, 46765813, 85184753, 272571133, 496493125, 1588660985, 2893773997, 9259394777, 16866150857, 53967707677, 98303131145

Offset

1,1

Comments

b - a = 23 is the fourth term in A058529. The values of a are in A117476.

Links

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

Formula

c(1)=37, c(2)=65, c(3)=205, c(4)=373, c(n) = 6*c(n-2) - c(n-4).

G.f.: -x*(17*x^3+17*x^2-65*x-37) / ((x^2-2*x-1)*(x^2+2*x-1)). [Colin Barker, Dec 17 2012]

Example

c(5) = 6*205 - 37 = 1193 and 832^2 + 855^2 = 1193^2 and 855-832=23 and gcd(832,855,1193)=1.

Crossrefs

Cf. A058529, A117476.

Sequence in context: A107142 A158018 A226697 * A145486 A319673 A121764

Adjacent sequences: A117472 A117473 A117474 * A117476 A117477 A117478

Keyword

nonn,easy

Author

Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006

Status

approved