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Search: id:A059690
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| A059690 |
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Number of distinct Cunningham chains of first kind whose initial prime (cf. A059453) falls into the interval [2^(n-1),2^n]. |
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2
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| 1, 2, 2, 2, 3, 5, 7, 13, 20, 31, 52, 83, 142, 242, 412, 742, 1308, 2294, 4040, 7327, 13253, 24255, 44306, 81700, 150401, 277335, 513705, 954847, 1780466, 3325009, 6224182
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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C. K. Caldwell, Cunningham Chains
W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains
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EXAMPLE
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a(11)=21 means that between 1024 and 2048 exactly 21 primes introduce Cunningham chains: {1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901, 1931, 1973, 2003}.
Their lengths are 2, 3 or 4. Thus the complete chains spread over more than one binary size-zone: e.g.{1409, 2819, 5639, 11279} The primes 1439 and 2879 also form a chain but 1439 is not at the beginning of that chain, 89 is.
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MATHEMATICA
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c = 0; k = 1; Do[ While[k <= 2^n, If[ PrimeQ[k] && !PrimeQ[(k - 1)/2] && PrimeQ[2k + 1], c++ ]; k++ ]; Print[c], {n, 1, 29}]
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CROSSREFS
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Cf. A023272, A023302, A023330, A005602, A007700, A053176, A059452-A059456, A059500, A057331, A059688, A007053, A036378, A029837, A007053.
Sequence in context: A126111 A122789 A014208 this_sequence A121256 A022867 A070610
Adjacent sequences: A059687 A059688 A059689 this_sequence A059691 A059692 A059693
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 06 2001
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 23 2002
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