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A030018 Coefficients in 1/(1+P(x)), where P(x) is the generating function of the primes. 9
1, -2, 1, -1, 2, -3, 7, -10, 13, -21, 26, -33, 53, -80, 127, -193, 254, -355, 527, -764, 1149, -1699, 2436, -3563, 5133, -7352, 10819, -15863, 23162, -33887, 48969, -70936, 103571, -150715, 219844, -320973, 466641, -679232, 988627, -1437185, 2094446, -3052743 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n+1)/a(n) => ~-1.456074948582689671... (see A072508). - Zak Seidov, Oct 01 2011

LINKS

Zak Seidov, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Backhouse's Constant

FORMULA

Apply inverse of "INVERT" transform to primes: INVERT: a's from b's in 1+Sum a_i x^i = 1/(1-Sum b_i x^i).

a(n) = -prime(n) - Sum_{i=1..n-1} prime(i)*a(n-i), for n > 0. - Derek Orr, Apr 28 2015

MATHEMATICA

max = 50; P[x_] := 1 + Sum[Prime[n]*x^n, {n, 1, max}]; s = Series[1/P[x], {x, 0, max}]; CoefficientList[s, x] (* Jean-Fran├žois Alcover, Sep 24 2014 *)

PROG

(PARI) v=[]; for(n=1, 50, v=concat(v, -prime(n)-sum(i=1, n-1, prime(i)*v[#v-i+1]))); v \\ Derek Orr, Apr 28 2015

CROSSREFS

Cf. A072508.

Sequence in context: A016732 A077948 A077971 * A010739 A166918 A143576

Adjacent sequences:  A030015 A030016 A030017 * A030019 A030020 A030021

KEYWORD

sign

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 10 11:39 EST 2016. Contains 279001 sequences.