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.

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

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=s-FactorInteger[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