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Search: id:A111145
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| A111145 |
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Length of the Cunningham chain initiated by the n-th Sophie Germain prime. |
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+0
1
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| 5, 2, 4, 3, 2, 2, 3, 2, 2, 6, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 4, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If a(n) is a high-water mark of this sequence, then A057331(a(n)) is the first term of the first Cunningham sequence of length a(n). For example, a(10)=6 is a high-water mark of this sequence, and A057331(a(10))=89 is the first term of the first Cunningham sequence of length 6.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
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a(10)=6 because 89, the 10th Sophie Germain prime, is the first term of the Cunningham chain 89, 179, 359, 719, 1439, 2879, which consists of 6 terms.
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MATHEMATICA
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lst=Select[Prime[Range[1000]], PrimeQ[2#+1]&]; Table[p=lst[[i]]; k=1; While[p=2p+1; PrimeQ[p], k++ ]; k, {i, Length[lst]}] - T. D. Noe (noe(AT)sspectra.com), Jun 06 2006
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CROSSREFS
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Cf. A005384, A057331.
Sequence in context: A073943 A019901 A083241 this_sequence A021660 A064853 A112597
Adjacent sequences: A111142 A111143 A111144 this_sequence A111146 A111147 A111148
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KEYWORD
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nice,nonn
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AUTHOR
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Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 18 2005
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jun 06 2006
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