A257743 Let n'= odd part of n. If n' is 1 or prime, then a(n)=1; otherwise a(n) is 1+ the number of times the map x -> (3*x+1)' must be applied to n' in order to reach 1 or a prime.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 8, 1, 3, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2

Offset

1,9

Comments

Conjecture: for every N>0 there exists n=n(N) such that a(n)>N.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Example

Let n=9. We have 9'=9; since (3*9+1)'=7, then a(9)=1+1=2.

Mathematica

oddPart:=#/2^IntegerExponent[#, 2]&;
a257743=Map[Length[NestWhileList[oddPart[3#+1]&, oddPart[#], !(PrimeQ[#]||#==1)&]]&, Range[200]] (*Peter J. C. Moses, May 07 2015*)

Prog

(PARI) step(n)=n>>=valuation(n, 2); if(isprime(n), 1, n)
a(n)=my(k=1); while((n=step(n))>1, n=3*n+1; k++); k \\ Charles R Greathouse IV, May 15 2015

Crossrefs

Cf. A000040, A000265.

Sequence in context: A356936 A257990 A369257 * A033272 A324907 A331295

Adjacent sequences: A257740 A257741 A257742 * A257744 A257745 A257746

Keyword

nonn

Author

Vladimir Shevelev, May 07 2015

Extensions

More terms from Peter J. C. Moses, May 07 2015

Status

approved