A274472 Number of iterations of the Collatz recursion required to reach a prime number.

2, 0, 0, 1, 0, 1, 0, 2, 3, 1, 0, 2, 0, 1, 2, 3, 0, 4, 0, 2, 6, 1, 0, 3, 3, 1, 2, 2, 0, 3, 0, 4, 6, 1, 2, 5, 0, 1, 2, 3, 0, 7, 0, 2, 4, 1, 0, 4, 3, 4, 6, 2, 0, 3, 2, 3, 3, 1, 0, 4, 0, 1, 17, 5, 6, 7, 0, 2, 5, 3, 0, 6, 0, 1, 2, 2, 4, 3, 0, 4, 3, 1, 0, 8, 8, 1, 2

Offset: 1

Author

Matthew Campbell, Jun 24 2016

Keywords

• nonn

Comments

If n is prime then a(n)=0. If n is composite then a(n)=A280929(n). - Dmitry Kamenetsky, Jan 11 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A000040, A006877, A280929.

Programs

Mathematica

Table[Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, ! PrimeQ@ # &] - 1, {n, 120}] (* Michael De Vlieger, Jun 26 2016 *)

PARI

a(n) = my(i=0, k=n); while(!ispseudoprime(k), if(k%2==0, k=k/2, k=3*k+1); i++); i
for(n=1, 87, print1(a(n), ", ")) \\ Felix Fröhlich, Jun 24 2016

Extensions

More terms from Felix Fröhlich, Jun 24 2016