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Search: id:A121497
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| A121497 |
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Binomial transform of the characteristic function of the prime numbers (A010051). |
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+0
2
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| 0, 1, 4, 10, 21, 41, 78, 148, 282, 537, 1013, 1882, 3446, 6267, 11468, 21416, 41209, 81771, 166042, 340994, 700570, 1429375, 2886777, 5771828, 11453105, 22638215, 44742141, 88681674, 176545766, 352992931, 707922077, 1421120880, 2849433326
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This is the binomial transform of the sequence {0,0,1,1,0,1,0,1,...}. Sequence A052467, the binomial transform of the sequence {0,1,1,0,1,0,1,...} is very similar. In fact, the first differences of this sequence yields A052467.
The number of pernicious numbers (A052294) less than 2^n. Although the graph looks almost like 2^n, the graph of a(n)/2^n has quite a bit of variation. - T. D. Noe, Mar 14 2009
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n)=sum_{i=1..pi(n)} binomial(n,prime(i)), where pi(n) is the number of primes <= n.
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MATHEMATICA
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Table[Sum[Binomial[n, Prime[i]], {i, PrimePi[n]}], {n, 40}]
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CROSSREFS
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Sequence in context: A024988 A144897 A001891 this_sequence A132925 A166553 A053643
Adjacent sequences: A121494 A121495 A121496 this_sequence A121498 A121499 A121500
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 03 2006
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