A323375 Let f(p, q) denote the pair (p + q, wt(p) + wt(q)). a(n) gives the number of iterations of f starting at (n, 1) needed to make p/q an integer, or if no integer is ever reached then a(n) = -1. (Here wt is binary weight, A000120.)

1, 3, 3, 3, 1, 2, 1, 11, 4, 10, 1, 3, 4, 9, 2, 19, 1, 18, 1, 1, 7, 17, 7, 7, 6, 5, 6, 6, 1, 4, 15, 5, 16, 4, 1, 2, 4, 3, 1, 14, 3, 13, 13, 13, 12, 12, 1, 6, 12, 2, 5, 5, 11, 1, 5, 13, 10, 4, 1, 12, 3, 9, 3, 3, 1, 2, 1, 1, 40, 2, 8, 8, 39, 3, 7, 7, 9, 2, 3, 1, 3, 37, 37, 37, 5, 36, 36, 3, 1, 8

Offset: 1

Author

Ctibor O. Zizka, Jan 12 2019

Keywords

• nonn
• base

Examples

			n=8; (8, 1) -> (9, 2) -> (11, 3) -> (14, 5) -> (19, 5) -> (24, 5) -> (29, 4) -> (33, 5) -> (38, 4) -> (42, 4) -> (46, 4) -> (50, 5). 50/5 = 10, so a(8) = 11 because it needs 11 iterations until p/q is an integer.
		

Crossrefs

Cf. A323275, A000120.

Programs

PARI

f(v) = return([v[1]+v[2], hammingweight(v[1])+hammingweight(v[2])]);
a(n) = {my(nb = 0, v = [n, 1]); while (1, v = f(v); nb++; if (frac(v[1]/v[2]) == 0, return (nb)));} \\ Michel Marcus, Jan 13 2019