login
A136349
Numbers k of the form Product_{j=1..m} prime(j) such that k-1 is prime.
10
6, 30, 2310, 30030, 304250263527210, 23768741896345550770650537601358310
OFFSET
1,1
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
FORMULA
a(n) = A057705(n) + 1 = A034386( A006794(n) ). - M. F. Hasler, May 02 2008
EXAMPLE
a(3)=30 where the prime factors are 2,3,5; since N-1=29, prime, N=30 is added to the sequence.
MATHEMATICA
Select[FoldList[Times, 1, Prime[Range[70]]], PrimeQ[#-1]&] (* Harvey P. Dale, Jan 09 2011 *)
PROG
(PARI) c=0; t=1; vector(7, n, until( ispseudoprime( -1+t*=prime(c++)), ); t)
CROSSREFS
KEYWORD
nonn
AUTHOR
Enoch Haga, Dec 25 2007
EXTENSIONS
Edited by M. F. Hasler, May 02 2008, May 30 2008
STATUS
approved