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 1-8 of 8 results.

A101985 Numbers that occur exactly once in A289493 (= number of primes between 2n and 3n).

Original entry on oeis.org

11, 42, 93, 110, 113, 156, 186, 196, 197, 220, 252, 292, 298, 362, 403, 429, 493, 503, 609, 644, 659, 727, 735, 778, 790, 886, 888, 920, 932, 952, 953, 1008, 1023, 1024, 1079, 1093, 1094, 1100, 1109, 1136, 1165, 1208, 1212, 1213, 1226, 1238, 1250, 1311
Offset: 1

Views

Author

Cino Hilliard, Jan 29 2005

Keywords

Crossrefs

Cf. A289493, A101984.

Programs

  • Mathematica
    f[n_] := PrimePi[3n] - PrimePi[2n]; t = Split[ Sort[ Table[ f[n], {n, 14000}] ]]; Flatten[ Select[t, Length[ # ] == 1 &]] (* Robert G. Wilson v, Feb 10 2005 *)
  • PARI
    bet2n3n(n)={ my(b=vecsort( vector(n,x, my(c=0); forprime(y=2*x+1,3*x-1, c++); c))); for(x=1,n-2, if(b[x+1]>b[x] && b[x+1]A289493 and/or primepi(3n)-primepi(2n) would be faster. Edited and corrected by M. F. Hasler, Sep 29 2019
  • PARI
    \\ Size of vector dependent on how pessimistic one is on smoothness of primepi
primecount(a, b)=primepi(b)-primepi(a);
v=vector(14000);
for(k=1, oo, j=primecount(2*k, 3*k); if(j>#v, break, v[j]++));
for(k=1, 1311, if(v[k]==1, print1(k, ", "))) \\ Hugo Pfoertner, Sep 29 2019

Extensions

More terms from Robert G. Wilson v, Feb 10 2005
Name edited by M. F. Hasler, Sep 29 2019

A289494 Number of primes in the interval [3n, 4n].

Original entry on oeis.org

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

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289495, A289496, A289497, A289498, A289499, A289500.

Programs

  • Mathematica
    Join[{1},Rest[Table[PrimePi[4n]-PrimePi[3n],{n,80}]]] (* Harvey P. Dale, Dec 30 2024 *)

A289495 Number of primes in the interval [4n, 5n].

Original entry on oeis.org

1, 0, 1, 2, 1, 1, 2, 1, 3, 3, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 4, 6, 6, 6, 5, 4, 4, 5, 4, 5, 6, 6, 6, 7, 6, 7, 8, 6, 8, 9, 8, 7, 8, 7, 7, 8, 9, 9, 9, 7, 8, 9, 9, 10, 11, 11, 12, 11, 11, 10, 9, 10, 11, 12, 11, 10, 11, 10, 10, 11, 10, 11, 11, 11, 12
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289496, A289497, A289498, A289499, A289500.

Programs

  • PARI
    a(n) = primepi(5*n) - primepi(4*n); \\ Michel Marcus, Jul 08 2017

A289496 Number of primes in the interval [5n, 6n].

Original entry on oeis.org

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

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289497, A289498, A289499, A289500.

Programs

A289497 Number of primes in the interval [6n, 7n].

Original entry on oeis.org

1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 5, 4, 2, 2, 4, 4, 4, 4, 5, 5, 6, 5, 5, 6, 5, 5, 5, 5, 5, 7, 7, 8, 7, 7, 7, 8, 8, 7, 7, 8, 8, 6, 6, 6, 8, 9, 8, 7, 8, 10, 10, 10, 10, 9, 9, 10, 11, 11, 10, 10, 12, 12, 12, 12, 12, 12, 13, 13, 11, 12, 12, 10, 9, 10, 10
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289498, A289499, A289500.

Programs

  • PARI
    a(n) = primepi(7*n) - primepi(6*n); \\ Michel Marcus, Jul 08 2017

A289498 Number of primes in the interval [7n, 8n].

Original entry on oeis.org

1, 0, 1, 2, 1, 2, 1, 2, 2, 3, 2, 1, 3, 4, 3, 2, 2, 4, 4, 3, 5, 4, 5, 4, 6, 4, 5, 4, 4, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 7, 5, 5, 6, 7, 7, 7, 8, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 11, 11, 11, 11, 10, 11, 11, 10, 10, 8, 9, 9, 9, 9, 9, 9, 10, 10, 12, 13, 14, 14, 13
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289499, A289500.

A289499 Number of primes in the interval [8n, 9n].

Original entry on oeis.org

0, 1, 0, 0, 2, 1, 2, 2, 2, 2, 2, 4, 3, 1, 2, 3, 4, 3, 3, 4, 3, 5, 4, 4, 2, 5, 6, 6, 5, 5, 6, 7, 6, 4, 6, 5, 5, 6, 6, 6, 7, 7, 8, 7, 7, 7, 8, 7, 8, 9, 9, 11, 9, 9, 9, 10, 10, 8, 8, 7, 8, 8, 7, 8, 9, 9, 11, 11, 13, 12, 12, 13, 13, 14, 13, 13, 13, 12, 12, 13
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289500.

A289500 Number of primes in the interval [9n, 10n].

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 4, 2, 1, 4, 3, 3, 3, 4, 3, 5, 4, 2, 4, 5, 5, 4, 4, 5, 6, 5, 4, 5, 4, 6, 5, 6, 6, 7, 7, 6, 7, 7, 6, 8, 8, 8, 9, 9, 8, 8, 9, 6, 8, 7, 7, 6, 7, 8, 8, 10, 10, 12, 11, 10, 12, 12, 11, 12, 10, 11, 12, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 12 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289499.
Cf. A038801.

Programs

  • Magma
    [0] cat [#PrimesInInterval(9*n, 10*n): n in [2..100]]; // Vincenzo Librandi, Jul 13 2017
  • Maple
    seq(numtheory:-pi(10*n)-numtheory:-pi(9*n),n=1..100); # Robert Israel, Jul 12 2017
  • Mathematica
    Join[{0}, Table[PrimePi[10 n] - PrimePi[9 n], {n, 2, 100}]] (* Vincenzo Librandi, Jul 13 2017 *)
  • PARI
    a(n) = primepi(10*n) - primepi(9*n); \\ Michel Marcus, Jul 12 2017

Formula

a(n) = n/log(n) + (1 + log(3^18/10^10))*n/log(n)^2 + O(n/log(n)^3) as n -> infinity. - Robert Israel, Jul 12 2017
Showing 1-8 of 8 results.

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