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

17, 8126654054401

Offset

1,1

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 (primes p such that 1 + product of primes up to p is prime) as indexed by A014545 (n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime). 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

Links

Table of n, a(n) for n=1..2.

Formula

{a(n)} = {1 + Prod[from i = 1 to n] A014613(i)} INTERSECTION {A000040}.

Example

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.

Crossrefs

Cf. A000040, A001358, A014612, A002110, A005234, A014545, A112141.

Sequence in context: A343778 A271562 A157255 * A134686 A257305 A128398

Adjacent sequences: A114429 A114430 A114431 * A114433 A114434 A114435

Keyword

nonn,bref

Author

Jonathan Vos Post, Feb 13 2006

Status

approved