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.

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

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 18,306-digit BPSW-probable prime is in fact prime.

Status

approved