

A101236


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


0



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

0,3


COMMENTS

(2^2)*31=11, (2^3)*31=23 and (2^4)*31=47 are primes so 3 is the third entry.
For every x in A001122, the xth 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

Table of n, a(n) for n=0..15.
Paul Jobling, NewPGen
G. Loeh, Long chains of nearly doubled primes, Mathematics of Computation, Vol. 53, No. 188, Oct 1989, pp. 751759.


CROSSREFS

Cf. A002515, A101790, A101794.
Sequence in context: A142600 A212999 A103980 * A119182 A178337 A161589
Adjacent sequences: A101233 A101234 A101235 * A101237 A101238 A101239


KEYWORD

hard,nonn


AUTHOR

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


EXTENSIONS

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


STATUS

approved



