OFFSET
0,2
COMMENTS
a(n+1)/a(n) => ~-1.456074948582689671... (see A072508). - Zak Seidov, Oct 01 2011
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..6124 (terms 0..1000 from Zak Seidov)
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
a(n) = Sum_{k=0..n} (-1)^k * A340991(n,k). - Alois P. Heinz, Feb 01 2021
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
-add(ithprime(n-i)*a(i), i=0..n-1))
end:
seq(a(n), n=0..70); # Alois P. Heinz, Jun 13 2018
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-François 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
KEYWORD
sign
AUTHOR
STATUS
approved