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Search: id:A095766
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| A095766 |
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Number of primes whose binary expansion begins '11' (A080166) in range ]2^n,2^(n+1)]. |
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5
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| 1, 1, 1, 2, 3, 7, 11, 21, 37, 67, 125, 227, 431, 787, 1491, 2812, 5296, 10055, 19079, 36343, 69398, 132661, 254122, 488028, 937994, 1806147, 3482463, 6722625, 12994889, 25145151, 48709705, 94451647, 183312229, 356089665, 692285717
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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I.e. number of primes p such that (2^n + 2^(n-1)) < p < 2^(n+1).
Ratio a(n)/A036378(n) converges as follows: 1, 0.5, 0.5, 0.4, 0.428571, 0.538462, 0.478261, 0.488372, 0.493333, 0.489051, 0.490196, 0.489224, 0.494266, 0.488213, 0.492079, 0.492556, 0.492697, 0.493134, 0.493827, 0.493885, 0.494513, 0.494605, 0.494682, 0.495049, 0.495214, 0.495412, 0.495563, 0.495699, 0.49585, 0.495984, 0.496113, 0.496237, 0.496346
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LINKS
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A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
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MATHEMATICA
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f[n_] := PrimePi[2^(n + 1)] - PrimePi[2^n + 2^(n - 1) - 1]; Array[f, 35] (* Robert G. Wilson v *)
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CROSSREFS
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a(n) = A036378(n)-A095765(n).
Sequence in context: A024367 A037078 A034431 this_sequence A126755 A034795 A108184
Adjacent sequences: A095763 A095764 A095765 this_sequence A095767 A095768 A095769
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 2004
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EXTENSIONS
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a(34) and a(35) from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006
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