OFFSET
1,1
COMMENTS
a(n) is the number of primes between prime(n) and 2*prime(n) inclusive. - Sean A. Irvine, Apr 18 2023
Also for x = Product_{i=n..n+k} A000040(i), the least k such that A003961(x) > 2*x. - Antti Karttunen, Dec 08 2024
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 2000 terms from Harry J. Smith]
FORMULA
a(n) = A035250(prime(n)).
a(n) = A070046(n) + 1. - Sean A. Irvine, Apr 18 2023
From Antti Karttunen, Dec 08 2024: (Start)
a(n) < A108227(n). [Assuming M. F. Hasler's interpretation in May 08 2017 comment in the latter]
(End)
EXAMPLE
a(10) = 7 as there are 7 primes between prime(10) = 29 and 58 = 29*2: 29, 31, 37, 41, 43, 47, 53.
MAPLE
A062134 := proc(n) numtheory:-pi(2*ithprime(n))-n+1; end; # N. J. A. Sloane, Oct 19 2024
[seq(A062134(n), n=1..100)];
MATHEMATICA
Table[PrimePi[2*Prime[n]] - n + 1, {n, 100}] (* Paolo Xausa, Oct 22 2024 *)
PROG
(PARI) a(n)={1 + primepi(2*prime(n)) - n} \\ Harry J. Smith, Aug 19 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 08 2001
EXTENSIONS
Definition clarified by N. J. A. Sloane, Oct 04 2024
STATUS
approved