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Search: id:A005602
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| A005602 |
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Smallest prime beginning a complete Cunningham chain of length n (of the first kind).
(Formerly M4885)
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+0
24
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| 13, 3, 41, 509, 2, 89, 1122659, 19099919, 85864769, 26089808579, 665043081119, 554688278429, 4090932431513069, 95405042230542329
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The word "complete" indicates each chain is exactly n primes long (i.e. the chain cannot be a subchain of another one). Except for a(1), each term, by definition, is a Sophie Germain prime (A005384) as is each element except the last in each chain; each element after the first in each chain is a safe prime (A005385), so interior elements are both.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. Loh [ Loeh ], Long chains of nearly doubled primes, Math. Comp., 53 (1989), 751-759.
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LINKS
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C. Caldwell, The Prime Number Glossary: Cunningham Chains.
W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains
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CROSSREFS
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Cf. (A005384 and A005385), A007700, A023272, A023302, A023330, A057331, A005603.
Sequence in context: A128154 A107806 A138965 this_sequence A155847 A010219 A056139
Adjacent sequences: A005599 A005600 A005601 this_sequence A005603 A005604 A005605
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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a(13) found by Jack Brennen; a(14) found by Paul Jobling (Paul.Jobling(AT)WhiteCross.com) [Oct 23 2000]
Better description from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 07 2004
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