

A180625


a(1) = 2; a(n) is twice the previous term if it is prime, otherwise the previous term minus its lowest prime factor plus one.


1



2, 4, 3, 6, 5, 10, 9, 7, 14, 13, 26, 25, 21, 19, 38, 37, 74, 73, 146, 145, 141, 139, 278, 277, 554, 553, 547, 1094, 1093, 2186, 2185, 2181, 2179, 4358, 4357, 8714, 8713, 17426, 17425, 17421, 17419, 34838, 34837, 34827
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OFFSET

1,1


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

2 is prime; 2 * 2 = 4. 4 is composite; 4  lpf(4) + 1 = 4  2 + 1 = 3. 3 is prime; 3 * 2 = 6. 6 is composite; 6  lpf(6) + 1 = 6  2 + 1 = 5.


MATHEMATICA

Join[{s=2}, Table[If[PrimeQ[s], s=2s, s=sFactorInteger[s][[1, 1]]+1]; s, {43}]]
NestList[If[PrimeQ[#], 2#, #FactorInteger[#][[1, 1]]+1]&, 2, 50] (* Harvey P. Dale, May 02 2012 *)


CROSSREFS

Cf. A020639.
Sequence in context: A034701 A091857 A232642 * A132340 A132666 A116533
Adjacent sequences: A180622 A180623 A180624 * A180626 A180627 A180628


KEYWORD

nonn


AUTHOR

Grant Garcia, Jan 21 2011


STATUS

approved



