A114432 Primes of the form 1 + product of the first k 4-almost primes A014613.

17, 8126654054401

Offset: 1

Author

Jonathan Vos Post, Feb 13 2006

Keywords

• nonn

Comments

The next term is too large to display here. - N. J. A. Sloane, Jul 30 2009

4-almost prime analog of primorial primes A005234 as indexed by A014545. In that sense, this sequence is indexed by (1, 8, ...). No more through product of first 16 of the 4-almost primes.

Terms are one more than the products of 4-almost primes up to 16, 81, 294, 513, 825, 1356, 1612, 2004, 2756, 7714, ... - Charles R Greathouse IV, Jul 28 2009

Examples

			a(1) = 17 because 1 + 16 = 1 + A014613(1) = 1 more than the first 4-almost prime is itself prime.
a(2) = 8126654054401 = 1 + (16 * 24 * 36 * 40 * 54 * 56 * 60 * 81) = 1 more than the product of the first 8 of the 4-almost primes and is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..8

Crossrefs

Cf. A000040, A014613, A005234, A014545.

Programs

Mathematica

Select[FoldList[Times, Select[Range[200], PrimeOmega[#] == 4 &]] + 1, PrimeQ] (* Amiram Eldar, Jul 20 2025 *)

Formula

{1 + Product_{i=1..k} A014613(i)} INTERSECTION A000040.