

A323275


Let f(p, q) denote the pair (p + q, wt(p) + wt(q)); a(n) is obtained by iterating f starting at (n, 1) until p/q is an integer (and then a(n) is that integer), or if no integer is ever reached then a(n) = 1. (Here wt is binary weight, A000120.)


3



1, 2, 2, 2, 2, 2, 2, 10, 7, 10, 3, 7, 5, 10, 7, 22, 6, 22, 5, 7, 8, 22, 10, 10, 8, 8, 10, 10, 6, 8, 22, 8, 22, 8, 9, 8, 10, 8, 8, 22, 10, 22, 22, 22, 22, 22, 8, 15, 22, 11, 15, 15, 22, 11, 16, 16, 22, 15, 10, 16, 15, 22, 15, 14, 22, 14, 17, 23, 40, 15, 22, 22, 40, 12, 22, 22, 16, 12, 18, 27, 18, 40, 40, 40, 22, 40, 14, 18, 34
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..89.
Jeffrey C. Lagarias, Wild and Wooley Numbers, arXiv preprint arXiv:math/0411141 [math.NT], 20042005.


EXAMPLE

(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 is an integer, so a(8) = 50/5 = 10.


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(q=v[1]/v[2]) == 0, return (q))); } \\ Michel Marcus, Jan 13 2019


CROSSREFS

Cf. A000120, A059175, A323375.
Sequence in context: A202448 A129381 A319991 * A139514 A330955 A330956
Adjacent sequences: A323272 A323273 A323274 * A323276 A323277 A323278


KEYWORD

nonn,base


AUTHOR

Ctibor O. Zizka, Jan 12 2019


STATUS

approved



