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Search: id:A023360
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| A023360 |
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Number of compositions of n into sums of primes. |
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+0
5
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| 1, 0, 1, 1, 1, 3, 2, 6, 6, 10, 16, 20, 35, 46, 72, 105, 152, 232, 332, 501, 732, 1081, 1604, 2352, 3493, 5136, 7595, 11212, 16534, 24442, 36039, 53243, 78573, 115989, 171264, 252754, 373214, 550863, 813251, 1200554, 1772207, 2616338, 3862121, 5701553
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 292-295.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
S. R. Finch, Kalmar's composition constant.
Philippe Flajolet, More information including asymptotic form (1995).
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 43, 298
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FORMULA
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a(n) = sum[a(n-p)] over primes p<=n with a(0)=1 - Henry Bottomley (se16(AT)btinternet.com), Dec 15 2000
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EXAMPLE
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2; 3; 4=2+2; 5=2+3=3+2; 6=2+2+2=3+3; 7=2+2+3=2+3+2=3+2+2=2+5=5+2; etc.
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MATHEMATICA
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CoefficientList[ Series[1 / (1 - Sum[ x^Prime[i], {i, 1, 15}]), {x, 0, 45}], x]
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CROSSREFS
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Cf. A000607 for the unordered (partition) version.
Sequence in context: A064684 A060408 A098071 this_sequence A154028 A157793 A096375
Adjacent sequences: A023357 A023358 A023359 this_sequence A023361 A023362 A023363
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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