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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A095391 a(n) is the least x such that A094892(x)=n.

Original entry on oeis.org

1751793, 235449, 60110, 10471, 17110, 8495, 6288, 3182, 2452, 1349, 331, 348, 446, 223, 249, 205, 111, 67, 55, 63, 28, 37, 14, 21, 18, 11, 10, 6, 551, 5, 4, 7, 3, 2
Offset: 0

Views

Author

Labos Elemer, Jun 16 2004

Keywords

Examples

			a[0]=1751793 because there are no primes between 210*1751793 and 210*1751794.
a[1]=235449 because there is one prime between 210*235449 and 210*235450.

Crossrefs

Cf. A078859, A095389, A008364.

Programs

  • Mathematica
    ta=Table[0, {up}]; Do[{m=0};Do[s=210*k+r; s1=210*k+r+2; If[PrimeQ[s], m=m+1], {r, 1, 210}];ta[[k]]=m, {k, 1, up}] Table[Min[Flatten[Position[ta, j]]], {j, 1, 48}]

Extensions

Edited by Don Reble, Jun 16 2004

A038822 Number of primes between 100n and 100n+99.

Original entry on oeis.org

25, 21, 16, 16, 17, 14, 16, 14, 15, 14, 16, 12, 15, 11, 17, 12, 15, 12, 12, 13, 14, 10, 15, 15, 10, 11, 15, 14, 12, 11, 12, 10, 11, 15, 11, 14, 13, 12, 11, 11, 15, 9, 16, 9, 11, 12, 12, 12, 8, 15, 12, 11, 10, 10, 13, 13, 12, 10, 16, 7, 12, 11, 13, 15, 8, 11, 10, 12, 12, 13, 9, 10
Offset: 0

Views

Author

Jeff Burch

Keywords

Comments

The number k first occurs in century A186311(k).

Examples

			a(3) = 16 because there are 16 primes between 300 and 399 (namely, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397).
a(4) = 17 because there are 17 primes between 400 and 499 (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499).

References

  • George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 91.

Links

Crossrefs

Cf. A028505.
Cf. A181098 (centuries without primes).
Cf. A186393-A186408 (centuries having 1 to 16 primes), A186509 (17 primes).
Cf. A094892, A098592.

Programs

  • Maple
    with(numtheory); A038822 := n->pi(100*n+99)-pi(100*n); seq(A038822(k), k=0..100); # Wesley Ivan Hurt, Oct 03 2013
  • Mathematica
    Table[PrimePi[100n + 99] - PrimePi[100n], {n, 0, 71}]
Differences[PrimePi[100 Range[0,100]]] (* Harvey P. Dale, Feb 18 2021 *)
  • PARI
    a(n)=sum(i=100*n,100*n+99,isprime(i)) \\ Charles R Greathouse IV, Apr 28 2015
  • PARI
    a(n)= my(r=0, p=100*n, q=p+99); while((p=nextprime(p+1))<=q, r+=isprime(p)); r; \\ Ruud H.G. van Tol, Nov 17 2024

Formula

a(n) = pi(100n+99) - pi(100n). - Wesley Ivan Hurt, Oct 03 2013

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jan 29 2003

A098592 Number of primes between n*30 and (n+1)*30.

Original entry on oeis.org

10, 7, 7, 6, 5, 6, 5, 6, 5, 5, 4, 6, 5, 4, 6, 5, 5, 2, 5, 5, 5, 6, 4, 4, 4, 5, 3, 6, 4, 4, 4, 4, 4, 5, 5, 4, 6, 3, 3, 4, 5, 4, 4, 6, 2, 3, 3, 5, 4, 7, 2, 5, 4, 6, 3, 4, 4, 3, 4, 4, 3, 2, 7, 3, 3, 3, 5, 5, 3, 5, 3, 5, 2, 3, 4, 4, 5, 3, 4, 7, 3, 4, 3, 1, 5, 3, 3, 3, 4, 7, 5, 4, 3, 5, 3, 4, 4, 3, 4, 2, 4, 3, 5, 2, 2, 3
Offset: 0

Views

Author

Hugo Pfoertner, Sep 16 2004

Keywords

Comments

Number of nonzero bits in A098591(n).
The number a(n) is < 8 except for n=0. - Pierre CAMI, Jun 02 2009
For references to positions where a(n) = 7 and related explanation, see A100418. - Peter Munn, Sep 06 2023

Examples

			a(1)=7 because there are 7 primes in the interval (30,60): 31,37,41,43,47,53,59.
a(26)=3 because the interval of length 30 following 26*30=780 contains 3 primes: 787, 797 and 809.

Links

Crossrefs

Cf. A000040 (prime numbers), A098591 (packed representation of the primes mod 30), A100418, A185641.
Cf. A038822, A094892.

Programs

  • FORTRAN
    ! See links given in A098591.
  • PARI
    a(n) = primepi(30*(n+1)) - primepi(30*n); \\ Michel Marcus, Apr 04 2020
  • Python
    from sympy import primerange
def a(n): return len(list(primerange(n*30, (n+1)*30)))
print([a(n) for n in range(106)]) # Michael S. Branicky, Oct 07 2021

Extensions

Edited by N. J. A. Sloane, Jun 12 2009 at the suggestion of R. J. Mathar
Showing 1-3 of 3 results.

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