A101236 Smallest i such that i*2^(2)-1, ..., i*2^(n+2)-1 are primes.

1, 1, 3, 45, 45, 15855, 280665, 4774980, 4393585185, 6522452145, 166260770280, 4321816939440, 15939674132892510, 22654052989616460555, 22654052989616460555, 202608454566431632290

Offset: 0

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004; revised Dec 31 2004

Keywords

• hard
• nonn

Comments

(2^2)*3-1=11, (2^3)*3-1=23 and (2^4)*3-1=47 are primes so 3 is the third entry.

For every x in A001122, the x-th term of this sequence and every succeeding term is divisible by x. For example 3 divides the 3rd and every succeeding term, 5 divides the 5th and every succeeding term.

The sequences of primes generated by these numbers are a type of Cunningham chain of the first kind (CC1). Since the longest known CC1 chain is of length 16, the next terms are currently unknown. - Douglas Stones (dssto1(AT)student.monash.edu.au), Mar 16 2005

Links

• Paul Jobling, NewPGen
• G. Loeh, Long chains of nearly doubled primes, Mathematics of Computation, Vol. 53, No. 188, Oct 1989, pp. 751-759.

Crossrefs

Cf. A002515, A101790, A101794.

Extensions

More terms from Douglas Stones (dssto1(AT)student.monash.edu.au), Mar 16 2005