A173978 Numbers n such that the least prime factor of 2n - 3 is less than that of 2n - 1, unless 2n - 3 and 2n - 1 are (twin) primes.

2, 6, 9, 12, 15, 18, 19, 21, 24, 27, 30, 33, 34, 36, 39, 40, 42, 45, 48, 49, 51, 54, 57, 60, 61, 63, 64, 66, 69, 72, 75, 78, 79, 81, 82, 84, 87, 90, 93, 94, 96, 99, 102, 105, 106, 108, 109, 111, 112, 114, 117, 120, 123, 124

Offset: 1

Author

Vladimir Shevelev, Mar 04 2010

Keywords

• nonn

Comments

Integers > 1 for which 2n - 3 is not in A001359 and A020639(2n-3) < A020639(2n-1).

Every multiple of 3 greater than 3 is in the sequence.

Examples

			a(3) = 9 because 2*9 - 3 = 15, the least prime factor of which is 3 and that is smaller than the least prime factor of 2*9 - 1 = 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639, A001359, A173977.

Programs

Mathematica

Select[Range[200], Not[PrimeQ[2# - 3] && PrimeQ[2# - 1]] && TrueQ[FactorInteger[2# - 3][[1, 1]] < FactorInteger[2# - 1][[1, 1]]] &] (* Alonso del Arte, Jun 05 2011 *)

Extensions

More terms from Alonso del Arte, Jun 05 2011