A094892 a(n) is the number of primes between n*210 and (n+1)*210.

46, 35, 33, 32, 30, 29, 27, 31, 27, 27, 26, 25, 30, 26, 22, 27, 26, 27, 24, 24, 26, 23, 26, 26, 22, 24, 26, 27, 20, 25, 23, 25, 23, 24, 22, 23, 26, 21, 21, 24, 21, 26, 24, 23, 25, 22, 25, 20, 25, 22, 21, 22, 21, 22, 21, 18, 26, 22, 21, 26, 23, 24, 22, 19, 21, 24, 21, 17, 23

Offset: 0

Author

Labos Elemer, Jun 16 2004

Keywords

• nonn

Comments

Arbitrarily long subsequences of consecutive 0's occur. a(n) is always <= 46. All values below 34 occur (see A095391); does 34?

Examples

			a(0) = 46 because there are 46 primes between 0*210 and 1*210.
a(1) = 35 because there are 35 primes between 1*210 and 2*210.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A008364, A038822, A078859, A095389, A098592.

Programs

Magma

[46] cat [#PrimesInInterval(210*n, 210*(n+1)): n in [1..80]]; // Vincenzo Librandi, Jul 08 2018

Mathematica

a[n_]:=PrimePi[210 (n + 1)] - PrimePi[210 n]; Table[a[n], {n, 0, 100}] (* Vincenzo Librandi, Jul 08 2018 *)

PARI

a(n) = primepi(210*(n+1)) - primepi(210*n); \\ Ruud H.G. van Tol, Oct 27 2024

PARI

a(n) = my(res = 0); forprime(p = n*210, (n+1)*210, isprime(p) && res++); res \\ David A. Corneth and Ruud H.G. van Tol, Oct 27 2024

Extensions

Edited by Don Reble, Jun 16 2004

Examples corrected by Matthew Vandermast, Jun 17 2004