A074727 - OEIS

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.

%I #10 Dec 15 2017 17:36:02

%S 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,

%T 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,

%U 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

%N 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.

%C Records appear at 2, 5, 8, 9, 14, 39, 62, 66, 73, 98, 722, 22226, 23226, 38737, 55411, ....

%C Can it be proved that a(n) > 0 for all n > 1?

%C What is a(55411)? If positive, it is greater than 35,000.

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

%K nonn,base

%O 2,4

%A _Jason Earls_, Sep 04 2002

%E Comments from _Charles R Greathouse IV_, Nov 18 2010.

%E a(55411) = 60796, assuming the 18,306-digit BPSW-probable prime is in fact prime.