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A280929 Number of steps required to reach the first prime when starting from n in the Collatz (or '3x+1') problem. 2
2, 3, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 4, 1, 2, 3, 3, 4, 2, 2, 6, 1, 4, 3, 3, 1, 2, 2, 4, 3, 2, 4, 6, 1, 2, 5, 5, 1, 2, 3, 3, 7, 8, 2, 4, 1, 2, 4, 3, 4, 6, 2, 6, 3, 2, 3, 3, 1, 2, 4, 4, 1, 17, 5, 6, 7, 2, 2, 5, 3, 2, 6, 5, 1, 2, 2, 4, 3, 4, 4, 3, 1, 6, 8, 8, 1, 2, 3, 3, 5, 2, 2, 6, 1, 15, 5, 3, 4, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n=p*2^k, where k>0 and p is some prime then a(n)=k.

If n is odd then a(n)=a(3n+1)+1.

If n is even then a(n)=1 or a(n)=a(n/2)+1.

If n is composite then a(n)=A274472(n).

LINKS

Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000

EXAMPLE

The Collatz iteration for 33 is 100, 50, 25, 76, 38, 19, 58, 29, ... 1. The first prime (19) is reached after 6 steps, so a(33)=6.

CROSSREFS

Cf. A006577, A274472.

Sequence in context: A060475 A168069 A334014 * A231725 A106559 A280047

Adjacent sequences:  A280926 A280927 A280928 * A280930 A280931 A280932

KEYWORD

nonn

AUTHOR

Dmitry Kamenetsky, Jan 11 2017

STATUS

approved

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)