cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Jun 16 2004

Keywords

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

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

A095392 Numbers n such that more than half of the reduced-residue system modulo 210 consists of primes in the following sense: in {210n + R} more than 24 = phi(210)/2 primes occur, i.e., 25-33, 35, 46.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20, 22, 23, 26, 27, 29, 31, 36, 41, 44, 46, 48, 56, 59, 70, 72, 74, 95, 109, 113, 114, 127, 132, 136, 148, 312, 321, 347, 428, 506, 538, 551, 1274, 1296, 1442, 2875, 4576, 5504, 6928, 7870, 12880, 15745, 17518
Offset: 1

Views

Author

Labos Elemer, Jun 16 2004

Keywords

Examples

			210n + r, where r runs through RRS of 210 corresponds to prime-difference patterns with several relatively small first prime differences.
n=18543: 210*18543 + r includes 26 primes with the following difference pattern: {2,4,2,4,30,18,2,10,6,12,2,18,6,10,2,12,12,4,6,8,6,6,4,2,10}.

Crossrefs

Cf. A095389, A095390, A095391.

Programs

  • Mathematica
    {k=0};Do[{m=0}; Do[s=210k+r; s1=210k+r+2;If[PrimeQ[s], m=m+1], {r, 1, 210}]; If[Greater[m, 24], Print[{m, k}]], {k, 0, 10000000}]

Formula

Solutions to A095390(x) > 24 = phi(210).
Showing 1-2 of 2 results.

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