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

Author

Grant Garcia, Jan 21 2011

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A020639.

Programs

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 *)