A114430 Primes of the form 1 + product of the first n 3-almost primes A014612.

97, 32920473601, 1448500838401, 65182537728001, 1491301685600774317670400000001, 48235157779343672198731287466250036763794299837586774072944798728192000000000000000001

Offset

1,1

Comments

3-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 (2, 8, 9, 10, 19, ...).

Links

Table of n, a(n) for n=1..6.

Formula

{a(n)} = {1 + Prod[from i = 1 to n] A014612(i)} INTERSECTION {A000040}.

Example

a(1) = 97 = 96 + 1 = 1 + (8 * 12) = 1 + A014612(1)*A014612(2) = 1 more than the product of the first 2 of the 3-almost primes and is prime.
a(2) = 32920473601 = 1 + (8 * 12 * 18 * 20 * 27 * 28 * 30 * 42) = 1 more than the product of the first 8 of the 3-almost primes and is prime.
a(3) = 1 more than the product of the first 9 of the 3-almost primes and is prime.
a(4) = 1 more than the product of the first 10 of the 3-almost primes and is prime.
a(5) = 1 more than the product of the first 19 of the 3-almost primes and is prime.

Mathematica

Select[Rest[FoldList[Times, 1, Select[Range[250], PrimeOmega[#]==3&]]]+1, PrimeQ] (* Harvey P. Dale, Dec 21 2013 *)

Crossrefs

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

Sequence in context: A322606 A145309 A122128 * A258765 A033418 A120310

Adjacent sequences: A114427 A114428 A114429 * A114431 A114432 A114433

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 13 2006

Extensions

One more term (a(6)) from Harvey P. Dale, Dec 21 2013

Status

approved