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A023360
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Number of compositions of n into prime parts.
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26
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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
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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.
Silvia Heubach and Toufik Mansour, Combinatorics of Compositions and Words, CRC Press, 2010.
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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, June 5, 2003. [Cached copy, with permission of the author]
Philippe Flajolet, More information including asymptotic form (1995). [Broken link]
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 43, 298
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FORMULA
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a(n) = Sum_{prime p<=n} a(n-p) with a(0)=1. - Henry Bottomley, Dec 15 2000
G.f.: 1/(1 - Sum_{k>=1} x^A000040(k)). - Andrew Howroyd, Dec 28 2017
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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, 15}]), {x, 0, 45}], x]
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PROG
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(PARI) {my(n=60); Vec(1/(1-sum(k=1, n, if(isprime(k), x^k, 0))) + O(x*x^n))} \\ Andrew Howroyd, Dec 28 2017
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CROSSREFS
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Cf. A000607 for the unordered (partition) version.
Sequence in context: A064684 A098071 A286970 * A154028 A157793 A096375
Adjacent sequences: A023357 A023358 A023359 * 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
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STATUS
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approved
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