A023657 - OEIS

%I #19 May 09 2021 10:57:55

%S 2,7,17,36,71,131,232,399,673,1124,1857,3049,4984,8117,13191,21408,

%T 34711,56239,91078,147455,238677,386284,625123,1011579,1636888,

%U 2648665,4285757,6934632,11220605,18155459,29376304,47532021,76908593,124440890,201349771

%N Convolution of (F(2), F(3), F(4), ...) and primes.

%H Indranil Ghosh, <a href="/A023657/b023657.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: (1/(1-x-x^2)-1)*b(x)/x, where b(x) is the g.f. of A000040. - _Mario C. Enriquez_, Mar 22 2017

%p a:= n-> add(ithprime(i)*combinat[fibonacci](n+2-i), i=1..n):

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Mar 22 2017

%t Table[Sum[Fibonacci[k + 1] Prime[n - k + 1], {k, n}], {n, 100}] (* _Indranil Ghosh_, Mar 22 2017 *)

%o (PARI) a(n) = sum(k=1, n, fibonacci(k+1)*prime(n-k+1)); \\ _Michel Marcus_, Mar 22 2017

%o (Python)

%o from sympy import prime, fibonacci

%o print([sum([fibonacci(k + 1) * prime(n - k + 1) for k in range(1, n + 1)]) for n in range(1, 101)]) # _Indranil Ghosh_, Mar 22 2017

%K nonn

%O 1,1

%A _Clark Kimberling_