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.

Showing 1-4 of 4 results.

A289493 Number of primes in the interval [2n, 3n].

Original entry on oeis.org

2, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 9, 10, 10, 9, 10, 10, 9, 10, 9, 9, 10, 9, 10, 10, 11, 12, 12, 12, 12, 13, 13, 14, 14, 13, 12, 13, 13, 13, 13, 13, 13, 14, 15, 14, 15
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289494, A289495, A289496, A289497, A289498, A289499, A289500.
Cf. A000720 (PrimePi), A101985 (numbers occurring here exactly once).

Programs

Formula

a(n) = A000720(3n) - A000720(2n), for n > 1. - M. F. Hasler, Sep 29 2019

A101909 Number of primes between 2n and 4n.

Original entry on oeis.org

1, 2, 2, 2, 4, 4, 3, 5, 4, 4, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 9, 10, 9, 10, 12, 12, 13, 14, 13, 12, 13, 14, 13, 15, 14, 13, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 21, 20, 19, 20, 19, 18, 19, 19, 20, 21, 22, 23, 23, 24, 23, 24, 24, 24, 26, 25, 25, 27, 27, 27, 28, 27, 26
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Links

Crossrefs

Cf. A101947, A101983, A101984, A101985.

Programs

  • Maple
    A101909 := proc(n::integer)
    numtheory[pi](4*n)-numtheory[pi](2*n) ;
end proc:
seq(A101909(n),n=1..100) ; # R. J. Mathar, Oct 02 2019
  • Mathematica
    f[n_] := PrimePi[4n] - PrimePi[2n]; Table[ f[n], {n, 76}] (* Robert G. Wilson v, Feb 10 2005 *)
  • PARI
    bet2n4n(n) = { local(c,x,y); forstep(x=2,n,2, c=0; forprime(y=x+1,x+x-1, c++; ); print1(c",") ) }
  • PARI
    s=0;vector(100,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1)) \\ Charles R Greathouse IV, Mar 12 2012

Formula

a(n) = A099802(2*n)-A099802(n). - R. J. Mathar, Oct 02 2019

A101947 A101909 sorted and duplicates removed.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Links

Crossrefs

Cf. A101909, A101983-A101985.

Programs

  • PARI
    bet2n4n(n) = { local(c,c1,x,y); a=vector(5001); for(x=1,n, c=0; forprime(y=2*x+1,4*x-1, c++; ); a[x] = c; ); b=vecsort(a); for(x=1,5000, if(b[x]>0, if(b[x]<>b[x+1],print1(b[x]",") ) ); ) }
  • PARI
    s=0;v=vectorsmall(10^6,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1));v=vecsort(v,,8);vecextract(v,Str("1..",#v\2)) \\ Charles R Greathouse IV, Mar 12 2012

A101984 Numbers that occur exactly once in A101909 (= count of primes between 2n and 4n).

Original entry on oeis.org

1, 3, 5, 8, 22, 36, 37, 46, 47, 48, 53, 63, 83, 98, 99, 101, 105, 108, 113, 114, 127, 135, 139, 148, 150, 155, 158, 171, 172, 173, 174, 175, 177, 178, 188, 205, 210, 218, 219, 220, 221, 226, 231, 240, 246, 254, 277, 282, 297, 298, 301, 303, 327, 333, 334, 339
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Examples

			There are 5 primes between 16 and 32 and nowhere else between 2n and 4n.

Crossrefs

Cf. A101909, A101947, A101983, A101985.

Programs

  • PARI
    bet2n4n(n)={ my(b=vecsort(vector(n,x, my(c=0); forprime(y=2*x+1,4*x-1, c++); c))); print1(1","); for(x=1,n-2, if(b[x+1]>b[x] && b[x+1]Don Reble. - M. F. Hasler, Sep 29 2019

Extensions

Better name from N. J. A. Sloane, Sep 29 2019
Corrected a(22) and a(45), following an observation by Don Reble. - M. F. Hasler, Sep 29 2019
Showing 1-4 of 4 results.

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