A334051 -id:A334051 - cp's OEIS frontend

A063124 a(n) = # { primes p | prime(n) <= p < 2*prime(n) } where prime(n) is the n-th prime.

2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 10, 10, 10, 10, 12, 14, 13, 14, 15, 14, 16, 16, 17, 20, 21, 20, 20, 19, 19, 24, 24, 26, 26, 28, 27, 29, 29, 29, 29, 31, 31, 33, 33, 33, 33, 36, 39, 39, 39, 40, 40, 40, 42, 43, 44, 43, 43, 43, 43, 43, 45, 50, 51, 50, 50, 55, 55, 57, 56, 56, 56, 58

Offset: 1

Reinhard Zumkeller, Aug 08 2001

nonn

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

			a(10) = 7 as there are 7 primes between prime(10) = 29 and 58 = 29*2: 29, 31, 37, 41, 43, 47, 53.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 2000 terms from Harry J. Smith]

Related sequences:
Primes (p) and composites (c): A000040, A002808, A000720, A065855.
Primes between p(n) and 2*p(n): A063124, A070046; between c(n) and 2*c(n): A376761; between n and 2*n: A035250, A060715, A077463, A108954.
Composites between p(n) and 2*p(n): A246514; between c(n) and 2*c(n): A376760; between n and 2*n: A075084, A307912, A307989, A376759.
Cf. A003961, A108227, A331677, A334051, A378746.

A062134 := proc(n) numtheory:-pi(2*ithprime(n))-n+1; end; # N. J. A. Sloane, Oct 19 2024
[seq(A062134(n),n=1..100)];

Table[PrimePi[2*Prime[n]] - n + 1, {n, 100}] (* Paolo Xausa, Oct 22 2024 *)

a(n)={1 + primepi(2*prime(n)) - n} \\ Harry J. Smith, Aug 19 2009

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) = n-A331677(n) = 1+n-A334051(n).
a(n) = 1+A000720(2*A000040(n))-n. [After Harry J. Smith's PARI-program]
a(n) < A108227(n). [Assuming M. F. Hasler's interpretation in May 08 2017 comment in the latter]
a(n) = A001222(A378746(n)).
(End)

Definition clarified by N. J. A. Sloane, Oct 04 2024

A331677 a(n) is the difference between the number of primes smaller than prime(n) (i.e., n-1) and greater than prime(n) but less than 2*prime(n).

Original entry on oeis.org

-1, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 2, 3, 4, 5, 4, 3, 5, 5, 5, 7, 6, 7, 7, 5, 5, 7, 8, 10, 11, 7, 8, 7, 8, 7, 9, 8, 9, 10, 11, 10, 11, 10, 11, 12, 13, 11, 9, 10, 11, 11, 12, 13, 12, 12, 12, 14, 15, 16, 17, 18, 17, 13, 13, 15, 16, 12, 13, 12, 14, 15, 16, 15, 15

Offset: 1

Todor Szimeonov, Jan 24 2020

sign

Cf. A000040, A000720, A020900, A070046, A334051.

a(n) = 2*n - 1 - primepi(2*prime(n)); \\ Michel Marcus, Feb 02 2020

a(n) = (2*n-1) - A020900(n). - Michel Marcus, Feb 02 2020
a(n) = n - 1 - A070046(n). - M. F. Hasler, Feb 29 2020
a(n) = A334051(n) - 1. - Alois P. Heinz, Oct 09 2020

cp's OEIS Frontend

A063124 a(n) = # { primes p | prime(n) <= p < 2*prime(n) } where prime(n) is the n-th prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions