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A110299
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a(n) = Sum_{i=0..n-1} 2^i*prime(n-i).
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5
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2, 7, 19, 45, 101, 215, 447, 913, 1849, 3727, 7485, 15007, 30055, 60153, 120353, 240759, 481577, 963215, 1926497, 3853065, 7706203, 15412485, 30825053, 61650195, 123300487, 246601075, 493202253, 986404613, 1972809335, 3945618783, 7891237693, 15782475517
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Eric Angelini, "Array with primes." Pers. comm. on the SeqFan mailing list, Sep. 7 2005.
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LINKS
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FORMULA
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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) = A007504(n) + Sum_{i=1..n-1} a(i). (End)
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 0, ithprime(n)+2*a(n-1))
end:
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MATHEMATICA
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Table[Sum[2^i * Prime[n-i], {i, 0, n-1}], {n, 1, 30}]
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PROG
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(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]]) >;
(SageMath)
def a(n): return 2 if (n==1) else 2*a(n-1) + nth_prime(n)
(Python)
from sympy import prime
c = 0
for i in range(n):
c = (c<<1)+prime(i+1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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