

A074727


Number of steps needed to reach a prime when the following map is repeatedly applied to n: if n is even then 2n + SOD(n) + 1, otherwise 2n  SOD(n)  1, where SOD(n) is the sum of the digits of n; or 1 if no prime is ever reached.


0



1, 1, 1, 2, 1, 2, 6, 7, 4, 1, 2, 4, 16, 1, 6, 6, 2, 3, 1, 3, 3, 6, 3, 5, 1, 2, 1, 2, 2, 2, 15, 1, 15, 1, 7, 3, 2, 21, 5, 15, 4, 16, 1, 8, 1, 7, 1, 2, 7, 7, 2, 1, 20, 2, 15, 1, 6, 1, 1, 8, 22, 2, 1, 20, 64, 3, 1, 31, 14, 22, 19, 66, 7, 1, 14, 1, 15, 10, 7, 2, 6, 19, 1, 4, 8, 2, 1, 7, 18, 3, 2, 1, 2
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OFFSET

2,4


COMMENTS

Records appear at 2, 5, 8, 9, 14, 39, 62, 66, 73, 98, 722, 22226, 23226, 38737, 55411, ....
Can it be proved that a(n) > 0 for all n > 1?
What is a(55411)? If positive, it is greater than 35,000.


LINKS

Table of n, a(n) for n=2..94.


EXAMPLE

a(10) = 4 because 10 > 22 > 49 > 84 > 181.


CROSSREFS

Sequence in context: A025277 A248100 A153896 * A059587 A070236 A020825
Adjacent sequences: A074724 A074725 A074726 * A074728 A074729 A074730


KEYWORD

nonn,base


AUTHOR

Jason Earls, Sep 04 2002


EXTENSIONS

Comments from Charles R Greathouse IV, Nov 18 2010.
a(55411) = 60796, assuming the 18,306digit BPSWprobable prime is in fact prime.


STATUS

approved



