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.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Example

For n=4: sequence is 2, 6, 3, 7, 11, 15, 5, 9, 3, 7, 11 ...
(2, 2+4, gpf(6), 3+4, 7+4, 11+4, gpf(15) etc.)
repeating period is (3, 7, 11, 15, 5, 9).
so a(4)=6.

Crossrefs

Sequence in context: A323621 A144216 A127938 * A033771 A033795 A222403

Adjacent sequences: A131987 A131988 A131989 * A131991 A131992 A131993

Keyword

easy,nonn

Author

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

Status

approved