A131990 - OEIS

A131990

Consider the periodic sequence S(n) defined by: b(1)=2, b(i+1) = b(i) + n if i is prime, b(i+1) = gpf(b(i)) if i is not prime, where gpf means "greatest prime factor"; then a(n) is the length of the repeating period of the sequence.

%I #1 Nov 10 2007 03:00:00

%S 3,2,3,6,5,2,4,5,7,9,4,8,6,2,3,8,8,14,6,10,5,4,4,7,6,5,15,11,15,2,4,8,

%T 10,12,4,11,8,15,4,7,6,18,6,5,11,10,4,10,8,11,5,10,4,5,6,11,23,25,5,

%U 14,8,2,6,14,12,30,10,8,14,12,4,9,10,19,22,17,14,12,6,6,27,7,14,10,4,11,8

%N Consider the periodic sequence S(n) defined by: b(1)=2, b(i+1) = b(i) + n if i is prime, b(i+1) = gpf(b(i)) if i is not prime, where gpf means "greatest prime factor"; then a(n) is the length of the repeating period of the sequence.

%e For n=4: sequence is 2, 6, 3, 7, 11, 15, 5, 9, 3, 7, 11 ...

%e (2, 2+4, gpf(6), 3+4, 7+4, 11+4, gpf(15) etc.)

%e repeating period is (3, 7, 11, 15, 5, 9).

%e so a(4)=6.

%K easy,nonn

%O 1,1

%A Paul Finley (pfinley(AT)touro.edu), Oct 07 2007