

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.


0



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
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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



