A338637 a(n) is the numerator of f(n) where f(n) = 1/n for n <= 2 and f(2n) = f(n-1)*f(n+1)+1, and f(2n+1) = f(n)*f(n+1)+1 for n > 2.

1, 1, 3, 5, 7, 9, 19, 29, 43, 53, 79, 149, 187, 293, 583, 849, 1311, 1601, 2343, 3525, 4315, 8025, 12027, 15029, 28119, 44169, 55303, 109533, 171843, 249781, 495991, 766361, 1115087, 1361297, 2103007, 3075769, 3755239, 5651717, 8267267, 10118237

Offset: 1

Author

William Phoenix Marcum, Nov 04 2020

Keywords

• nonn
• frac

Examples

			f(1) = 1/1, so a(1) = 1.
f(2) = 1/2, so a(2) = 1.
f(3) = f(1) * f(2) + 1 = 3/2, so a(3) = 3.
f(4) = f(1) * f(3) + 1 = 1 * 3/2 + 1 = 5/2, so a(4) = 5.
f(5) = f(2) * f(3) + 1 = 1/2 * 3/2 + 1 = 7/4, so a(5) = 7.
f(n) for n>=1: 1, 1/2, 3/2, 5/2, 7/4, 9/4, 19/4, 29/8, 43/8, 53/8, 79/16, 149/16, 187/16, 293/32, 583/32, 849/32 ...
		

Links

• Georg Fischer, Table of n, a(n) for n = 1..1000

Crossrefs

Denominators are given in A173862.

Programs

PARI

f(n) = if (n<=2, 1/n, my(x=n\2); if (n%2, f(x)*f(x+1)+1, f(x-1)*f(x+1)+1));
a(n) = numerator(f(n)); \\ Michel Marcus, Nov 05 2020