A063268 Let f be a function on rationals p/q (p,q coprime) defined by f(p/q) = abs(p-q)/g(p), where g(p) is the next odd number (starting with p) that we get after iteration of h(n) = n/2 when n is even, 5n-1 when n is odd. Start with f(n/1) and iterate f until it reaches again an integer, which is a(n). If no integer is reached, then a(n)=0.

0, 1, 5, 3, 1, 1, 19, 7, 3, 7, 3, 19, 12, 6, 41, 15, 5, 13, 7, 35, 15, 5, 21, 9, 13, 31, 41, 4, 55, 1, 85, 31, 9, 25, 2, 17, 4, 1, 8, 9, 7, 15, 5, 75, 5, 33, 43, 7, 10, 7, 15, 15, 6, 19, 15, 4, 29, 17, 3, 65, 31, 23, 173, 63, 17, 49, 4, 43, 23, 3, 55, 17, 9, 7, 25, 19, 8, 71, 47, 5, 3, 9

Offset

1,3

Comments

n=333 is the smallest n>1 with a(n)=0.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Example

For n=6, we get 6/1 -> 5/3 -> 2/3 -> 1/1 so a(6)=1.
For n=333, we get 333/1 -> 332/13 -> 319/83 -> 236/797 -> 561/59 -> 502/701 -> 199/251 -> 52/497 -> 445/13 -> 432/139 -> 293/27 -> 266/183 -> 83/133 -> 50/207 -> 157/25 -> 132/49 -> 83/33 -> 50/207 so a(333)=0.

Prog

(PARI) h(n) = if (n%2, 5*n-1, n/2);
g(n) = {n = h(n); while (!(n%2), n = h(n)); n; }
f(n) = {my(p = numerator(n), q = denominator(n)); abs(p-q)/g(p); }
a(n) = {my(v = []); for (k=1, oo, n = f(n); if (denominator(n) == 1, return(n)); if (#select(x->(x==n), v) > 0, return(0)); v = concat(v, n); ); } \\ Michel Marcus, Mar 23 2020

Crossrefs

Cf. A062366, A063256, A063257.

Sequence in context: A204063 A132400 A232810 * A179613 A196613 A151903

Adjacent sequences: A063265 A063266 A063267 * A063269 A063270 A063271

Keyword

nonn

Author

Floor van Lamoen, Jul 12 2001

Status

approved