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Search: id:A036378
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| A036378 |
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Number of primes p such that 2^n < p <= 2^(n+1). |
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+0
83
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| 1, 1, 2, 2, 5, 7, 13, 23, 43, 75, 137, 255, 464, 872, 1612, 3030, 5709, 10749, 20390, 38635, 73586, 140336, 268216, 513708, 985818, 1894120, 3645744, 7027290, 13561907, 26207278, 50697537, 98182656, 190335585, 369323305, 717267168, 1394192236
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of primes whose binary order (A029837) is n, i.e. those with ceiling[ Log[ 2,p ] ] = n.
First differences of A007053. This sequence illustrates how far the Bertrand postulate is oversatisfied.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..74 (using data from A007053)
Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
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EXAMPLE
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The 7 primes for which A029837(p)=6 are 37,41,43,47,53,59,61.
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MATHEMATICA
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t = Table[PrimePi[2^n], {n, 0, 20}]; Rest@t - Most@t (* Robert G. Wilson v *)
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CROSSREFS
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a(n) = A095005(n)+A095006(n) = A095007(n) + A095008(n) = A095013(n) + A095014(n) = A095015(n) + A095016(n) (for n > 1) = A095021(n)+A095022(n)+A095023(n)+A095024(n) = A095019(n)+A095054(n) = A095020(n)+A095055(n) = A095060(n)+A095061(n) = A095063(n)+A095064(n) = A095094(n)+A095095(n).
Sequence in context: A095333 A095326 A095330 this_sequence A028303 A047083 A035085
Adjacent sequences: A036375 A036376 A036377 this_sequence A036379 A036380 A036381
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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)
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu), May 13 2004
Entries checked by Robert G. Wilson v (rgwv(at)rgwv.com), Mar 20 2006
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