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 1-3 of 3 results.

A245098 The np values for distinct terms of A246783.

Original entry on oeis.org

1, 5, 11, 11, 16, 14, 20, 23, 21, 22, 31, 25
Offset: 1

Views

Author

Robert Price, Nov 12 2014

Keywords

Comments

See A246783 for a more complete description of this sequence.

Examples

			a(2)=5 because the second distinct term of A246783 is 67 and np(67)=5.
		

Crossrefs

A245101 The np values for terms in A246783.

Original entry on oeis.org

1, 1, 1, 1, 5, 5, 5, 5, 5, 11, 11, 11, 16, 14, 14, 20, 20, 23, 21, 22, 31, 25
Offset: 1

Views

Author

Robert Price, Nov 12 2014

Keywords

Comments

See A246783 for a more complete description of this sequence.

Examples

			a(6)=5 because A246783(6)=67 and np(67)=5.
		

Crossrefs

Cf. A246783.

A246810 a(n) is the smallest number m such that np(m) = n, where np(m) is number of primes p such that prime(m) < p < prime(m)^(1 + 1/m).

Original entry on oeis.org

1, 5, 12, 17, 25, 55, 83, 169, 207, 206, 384, 953, 1615, 2192, 2197, 3024, 3023, 10709, 10935, 29509, 29508, 62736, 62735, 94333, 94332, 196966, 314940, 608777, 1258688, 1767259, 2448975, 2448973, 7939362, 9373136, 9373134, 16854966, 16854967
Offset: 1

Views

Author

Keywords

Comments

Firoozbakht's conjecture says that for every n, there exists at least one prime p where, prime(n) < p < prime(n)^(1 + 1/n). Hence if Firoozbakht's conjecture is true, then there is no m such that np(m) = 0.
Conjecture: For every positive integer n, a(n) exists.
a(65) > 10^12. - Robert Price, Nov 12 2014

Examples

			a(6) = 55 since the number of primes p such that prime(55) < p < prime(55)^(1 + 1/55) is 6 and 55 is the smallest number with this property.
		

Crossrefs

Programs

  • Mathematica
    np[n_]:=(b=Prime[n]; Length[Select[Range[b+1, b^(1 + 1/n)],PrimeQ]]); a[n_]:=(For[m=1, np[m] !=n, m++]; m);
    Do[Print[a[n]], {n, 37}]
Showing 1-3 of 3 results.