OFFSET
1,1
REFERENCES
Eric Angelini, "Array with primes." Pers. comm. on the SeqFan mailing list, Sep. 7 2005.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
G.f: b(x)/(1-2*x), where b(x) is the g.f. of A000040. - Mario C. Enriquez, Dec 10 2016
a(n) = 2*a(n-1) + A000040(n) for n>0 with a(0)=0. - Alois P. Heinz, Dec 10 2016
From Ridouane Oudra, Jan 25 2024: (Start)
a(n) = Sum_{i=0..prime(n+1)-1} (2^(n-pi(i)) - 1), where prime(n) = A000040(n) and pi(n) = A000720(n).
a(n) = Sum_{i=1..n} A125180(i);
a(n) = A007504(n) + Sum_{i=1..n-1} a(i). (End)
MAPLE
a:= proc(n) option remember;
`if`(n=0, 0, ithprime(n)+2*a(n-1))
end:
seq(a(n), n=1..30); # Alois P. Heinz, Dec 10 2016
MATHEMATICA
Table[Sum[2^i * Prime[n-i], {i, 0, n-1}], {n, 1, 30}]
PROG
(PARI) a(n) = fromdigits(primes(n), 2); \\ Kevin Ryde, Jun 22 2022
(Magma)
A110299:= func< n | (&+[2^(n-j)*NthPrime(j): j in [1..n]]) >;
[A110299(n): n in [1..40]]; // G. C. Greubel, Jan 03 2023
(SageMath)
@CachedFunction # a = A110299
def a(n): return 2 if (n==1) else 2*a(n-1) + nth_prime(n)
[a(n) for n in range(1, 41)] # G. C. Greubel, Jan 03 2023
(Python)
from sympy import prime
def A110299(n):
c = 0
for i in range(n):
c = (c<<1)+prime(i+1)
return c # Chai Wah Wu, Jan 04 2023
KEYWORD
nonn,easy
AUTHOR
Ryan Propper, Sep 07 2005
STATUS
approved