A260712 Number of iterations of A234742 needed when started from n before a fixed point is reached.

0, 0, 0, 0, 6, 0, 0, 0, 5, 6, 0, 0, 0, 0, 5, 0, 4, 5, 0, 6, 4, 0, 55, 0, 0, 0, 4, 0, 141, 5, 0, 0, 140, 4, 1, 5, 0, 0, 54, 6, 0, 4, 2, 0, 145, 55, 0, 0, 3, 0, 6, 0, 2, 4, 0, 0, 1, 141, 0, 5, 0, 0, 3, 0, 2, 140, 0, 4, 4, 1, 4, 5, 0, 0, 1, 0, 2, 54, 5, 6, 3, 0, 3, 4, 4, 2, 0, 0, 4, 145, 0, 55, 139, 0, 1, 0, 0, 3, 53, 0, 3, 6, 0, 0, 3, 2, 14, 4, 0

Offset

1,5

Comments

The fixed points of A234742 are in A235035, thus the latter gives the zeros of this sequence.

It is not known whether the sequence is well-defined for all values. For example, does a(455) or a(1361) have a finite value? Cf. sequences A260735 and A260441.

Links

Antti Karttunen, Table of n, a(n) for n = 1..454

Formula

If A234742(n) = n, then a(n) = 0, otherwise a(n) = 1 + a(A234742(n)).

Other identities:

a(A235035(n)) = 0.

a(2n) = a(n).

Prog

(PARI)
allocatemem((2^30));
A234742(n) = factorback(subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2)); \\ After M. F. Hasler's Feb 18 2014 code.
A260712(n) = {my(prev=-1, i=-1); until((n==prev), prev = n; n = A234742(n); i++); return(i); };
for(n=1, 454, write("b260712.txt", n, " ", A260712(n)));
(Scheme, two alternatives, the first one using memoizing definec-macro)
(definec (A260712 n) (let ((next (A234742 n))) (if (= next n) 0 (+ 1 (A260712 next)))))
(define (A260712loop n) (let loop ((n (A234742 n)) (prev_n n) (i 0)) (if (= n prev_n) i (loop (A234742 n) n (+ 1 i)))))

Crossrefs

Cf. A235035 (gives the positions of zeros).

Cf. A234742, A260735, A260735, A260441.

Subsequences: A260713, A260716.

Sequence in context: A226784 A281319 A174431 * A173066 A173452 A282212

Adjacent sequences: A260709 A260710 A260711 * A260713 A260714 A260715

Keyword

nonn

Author

Antti Karttunen, Aug 04 2015

Status

approved