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A084143 Number of partitions of n into a sum of two or more consecutive primes. 8
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; refs; listen; history; text; internal format)
OFFSET

1,36

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

Eric Weisstein's World of Mathematics, Prime Sums

FORMULA

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, Mar 30 2006

EXAMPLE

a(36)=2 because we have 36=17+19=5+7+11+13.

MAPLE

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, Mar 30 2006

MATHEMATICA

max = 25; gf = Sum[ Sum[ Product[ x^Prime[k], {k, i, j}], {j, i+1, max}], {i, 1, max}]; Rest[ CoefficientList[gf, x]][[1 ;; 75]] (* Jean-Fran├žois Alcover, Oct 23 2012, after Emeric Deutsch *)

CROSSREFS

Cf. A084146, A084147.

Sequence in context: A321445 A007423 A076544 * A025888 A145708 A138532

Adjacent sequences:  A084140 A084141 A084142 * A084144 A084145 A084146

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, May 15 2003

STATUS

approved

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Last modified January 17 23:12 EST 2019. Contains 319251 sequences. (Running on oeis4.)