A323275 - OEIS

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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.)

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], 2004-2005.

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: A339165 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