A114428 Primes of the form 1 + product of the first n semiprimes.

5, 2161, 30241, 453601, 4495130640001, 152834441760001, 911300420785759804800001, 19660095637340203930960075575675174251117567173124497920000000001

Offset: 1

Author

Jonathan Vos Post, Feb 13 2006

Keywords

• nonn

Comments

Semiprime 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, 4, 5, 6, 11, 12, 39, ...).

The next term has 90 digits. - Harvey P. Dale, Sep 21 2011

Examples

			a(1) = 5 = 4 + 1 = 1 + A001358(1) = 1 + A112141(1) because 4 is the first semiprime and 5 is prime.
a(2) = 2161 because 2160 + 1 = 1 + A001358(1)*A001358(2)*A001358(3)*A001358(4) = 1 + A112141(4) = 1 + (4*6*9*10) is prime.
a(3) = 1 + A112141(5).
a(4) = 1 + A112141(6).
a(5) = 1 + A112141(11).
a(6) = 1 + A112141(12).
a(7) = (4 * 6 * 9 * 10 * 14 * 15 * 21 * 22 * 25 * 26 * 33 * 34 * 35 * 38 * 39 * 46 * 49 * 51 * 55 * 57 * 58 * 62 * 65 * 69 * 74 * 77 * 82 * 85 * 86 * 87 * 91 * 93 * 94* 95 * 106 * 111 * 115 * 118 * 119) + 1 is prime.
		

Crossrefs

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

Programs

Mathematica

Select[#+1&/@FoldList[Times,1,Select[Range[200],PrimeOmega[#] == 2&]], PrimeQ] (* Harvey P. Dale, Sep 21 2011 *)

Formula

{a(n)} = {1 + A112141} INTERSECTION {A000040}.

Extensions

a(7) added by Jonathan Vos Post, Dec 12 2010