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Search: id:A101236
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| A101236 |
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Smallest i such that i*2^(2)-1, ..., i*2^(n+2)-1 are primes. |
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1
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| 1, 1, 3, 45, 45, 15855, 280665, 4774980, 4393585185, 6522452145, 166260770280, 4321816939440, 15939674132892510, 22654052989616460555, 22654052989616460555, 202608454566431632290
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OFFSET
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0,3
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COMMENT
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(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 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
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REFERENCES
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G. Loeh, Long Chains of Nearly Doubled Primes, Mathematics of Computation, Vol. 53, No. 188, Oct 1989, pp. 751-759.
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LINKS
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Paul Jobling, NewPGen
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CROSSREFS
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Cf. A002515, A101790, A101794.
Sequence in context: A102811 A142600 A103980 this_sequence A117960 A119182 A079038
Adjacent sequences: A101233 A101234 A101235 this_sequence A101237 A101238 A101239
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KEYWORD
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hard,nonn
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004; revised Dec 31, 2004
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EXTENSIONS
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More terms from Douglas Stones (dssto1(AT)student.monash.edu.au), Mar 16 2005
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