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Search: id:A084143
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| A084143 |
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Number of partitions of n into a sum of two or more consecutive primes. |
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+0
6
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| 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1
(list; graph; listen)
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OFFSET
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1,36
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Prime Sums
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FORMULA
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G.f.=sum(sum(product(x^p(k), k=i..j), j=i+1..infinity), i=1..infinity), where p(k) is the k-th prime. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(36)=2 because we have 36=17+19=5+7+11+13.
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MAPLE
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g:=sum(sum(product(x^ithprime(k), k=i..j), j=i+1..25), i=1..25): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Cf. A084146, A084147.
Sequence in context: A072453 A007423 A076544 this_sequence A025888 A138532 A145708
Adjacent sequences: A084140 A084141 A084142 this_sequence A084144 A084145 A084146
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), May 15, 2003
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