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A121497
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Binomial transform of the characteristic function of the prime numbers (A010051).
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3
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| 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
| Table[Sum[Binomial[n, Prime[i]], {i, PrimePi[n]}], {n, 40}]
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CROSSREFS
| Sequence in context: A024988 A144897 A001891 * A132925 A053643 A111927
Adjacent sequences: A121494 A121495 A121496 * A121498 A121499 A121500
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Aug 03 2006
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