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

1,2

Links

Table of n, a(n) for n=1..90.

Example

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.

Prog

(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

Crossrefs

Cf. A323275, A000120.

Sequence in context: A119560 A172364 A323596 * A140366 A167817 A153401

Adjacent sequences: A323372 A323373 A323374 * A323376 A323377 A323378

Keyword

nonn,base

Author

Ctibor O. Zizka, Jan 12 2019

Status

approved