A136349 Numbers k of the form Product_{j=1..m} prime(j) such that k-1 is prime.

6, 30, 2310, 30030, 304250263527210, 23768741896345550770650537601358310

Offset: 1

Author

Enoch Haga, Dec 25 2007

Keywords

• nonn

Comments

This sequence is different from A121069 and A002110.

Compute the product of k consecutive sequences of prime factors 2,3,5,7, etc. where k=1,2,3,4,5, etc. When N is preceded by prime N-1 add N to the sequence.

a(7) = 1 9361386640 7008231634 7142505431 2320082662 8976125715 6376190696 2414215012 3698566371 7909694733 5243680669 6075314756 2914824028 4399976570 - copied from Data field by Michael B. Porter, Mar 30 2013

Next term (a(8)) is too large to be included: see A006794. - M. F. Hasler, May 02 2008

The next 7 terms in the sequence are a(7) = p# 2..89 (shown in full above), a(8) = p# 2..317, a(9) = p# 2..337, a(10) = p# 2..991, a(11) = p# 2..1873, a(12) = p# 2..2053, a(13) = p# 2..2377, where p# indicates a primorial. - Jeff Hall, Apr 05 2021

Examples

			a(3)=30 where the prime factors are 2,3,5; since N-1=29, prime, N=30 is added to the sequence.
		

Crossrefs

Cf. A136350, A136351, A136352, A002110, A121069.

Programs

Mathematica

Select[FoldList[Times,1,Prime[Range[70]]],PrimeQ[#-1]&]  (* Harvey P. Dale, Jan 09 2011 *)

PARI

c=0;t=1;vector(7,n,until( ispseudoprime( -1+t*=prime(c++)),);t)

Formula

a(n) = A057705(n) + 1 = A034386( A006794(n) ). - M. F. Hasler, May 02 2008

Extensions

Edited by M. F. Hasler, May 02 2008, May 30 2008