A014692 a(n) = prime(n) - (n-1).

2, 2, 3, 4, 7, 8, 11, 12, 15, 20, 21, 26, 29, 30, 33, 38, 43, 44, 49, 52, 53, 58, 61, 66, 73, 76, 77, 80, 81, 84, 97, 100, 105, 106, 115, 116, 121, 126, 129, 134, 139, 140, 149, 150, 153, 154, 165, 176, 179, 180, 183, 188, 189, 198, 203, 208, 213, 214, 219, 222, 223

Offset: 1

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Comments

Also, number of primes between prime(n) and prime(prime(n)) inclusive. For example, prime(1) = 2, prime(prime(1)) = prime(2) = 3 and there are two primes between 2 and 3 inclusive. - Zak Seidov, Sep 22 2003; N. J. A. Sloane, Mar 07 2007

Since a(n+1) - a(n) = prime(n+1) - prime(n) - 1 >= 1 for n > 1, the sequence is monotonic for n > 1. - N. J. A. Sloane, Mar 07 2007

a(n) = number of terms < prime(n) in A141468. - David James Sycamore, Oct 14 2017

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A141468.

Equals A014689 + 1.

Programs

Maple

A014692:=n->ithprime(n)-(n-1): seq(A014692(n), n=1..100); # Wesley Ivan Hurt, Oct 15 2017

Mathematica

Table[Prime[n] - n + 1, {n, 61}]  (* Geoffrey Critzer, May 02 2013 *)

PARI

first(n) = {my(t, res = vector(n)); forprime(p=2, , t++; res[t] = p - t + 1; if(t>=n, return(res)))} \\ David A. Corneth, Oct 04 2017

PARI

a(n) = prime(n)-n+1; \\ Altug Alkan, Oct 05 2017

Python

from sympy import prime
def A014692(n): return prime(n)-n+1 # Chai Wah Wu, Oct 11 2024

Extensions

More terms from Andrew J. Gacek (andrew(AT)dgi.net)