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.

A079953 Smallest prime p such that prime(n) mod 2*p = prime(n).

Original entry on oeis.org

2, 2, 3, 5, 7, 7, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 31, 31, 37, 37, 37, 41, 43, 47, 53, 53, 53, 59, 59, 59, 67, 67, 71, 71, 79, 79, 79, 83, 89, 89, 97, 97, 97, 97, 101, 101, 107, 113, 127, 127, 127, 127, 127, 127, 131, 137, 137, 137, 139, 149, 149, 149, 157, 157
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

Comments

a(n) is smallest prime greater than prime(n)/2. - Peter Munn, Sep 18 2017

Examples

			n=6: prime(6)=13 and 13 mod(2*2)=1, 13 mod(2*3)=1, 13 mod(2*5)=3, 13 mod(2*7)=13, therefore a(6)=7.

Links

Crossrefs

Cf. A079952, A039734.

Programs

  • Mathematica
    f[n_] := Block[{p = 2}, While[Prime@ n != Mod[Prime@ n, 2 p], p = NextPrime@ p]; p]; Array[f, 64] (* Michael De Vlieger, Mar 17 2015 *)
  • PARI
    a(n,q=prime(n))=nextprime(q/2) \\ Charles R Greathouse IV, Mar 17 2015

Formula

T(n, A049084(a(n))) = A000040(n), T defined as in A079950.
a(n) = nextprime(prime(n)/2) ~ (n log n)/2. - Charles R Greathouse IV, Mar 17 2015
Conjecture: a(n) = A039734(n), n>=2. - R. J. Mathar, May 03 2021

A079952 Number of primes less than prime(n)/2.

Original entry on oeis.org

0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 13, 14, 15, 15, 15, 16, 16, 16, 18, 18, 19, 19, 21, 21, 21, 22, 23, 23, 24, 24, 24, 24, 25, 25, 27, 29, 30, 30, 30, 30, 30, 30, 31, 32, 32, 32, 33, 34, 34, 34, 36, 36, 36, 37, 38, 39, 40
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

Comments

Previous name: Number of primes p such that prime(n) mod 2*p < prime(n).
Same as A055930, except for a(2). [Noticed by R. J. Mathar, Dec 15 2008, proved by Andrey Zabolotskiy, Oct 26 2017]

Examples

			n = 6: prime(6) = 13 and 2, 3, 5 are less than 13/2, therefore a(6) = 3.

Crossrefs

Cf. A000040, A000720, A055377, A055930, A079951, A079953, A217564.

Programs

Formula

A079950(n, a(n) + 1) = prime(n).
Where defined, that is for n > 2, prime(a(n)) = A055377(prime(n)). - Peter Munn, Sep 18 2017
0 with partial sums of A217564. - David A. Corneth, Oct 26 2017 (found earlier by Peter Munn).

Extensions

New name from Peter Munn, Sep 18 2017

A079951 Number of primes p with prime(n) == 1 (modulo 2*p).

Original entry on oeis.org

0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 1, 2, 1, 3, 2, 2, 2, 2, 3, 2, 1, 3, 2, 2, 3, 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 4, 2, 2, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 1, 2, 3, 2, 3, 3, 2, 1, 2, 3
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

Examples

			n=6: prime(6)=13 and 13 mod (2*2) = 1, 13 mod (2*3) = 1, 13 mod(2*5) = 3, 13 mod (2*7) = 13, therefore a(6)=2.

Crossrefs

Cf. A001221, A079950, A079952.

Programs

  • Mathematica
    Table[PrimeNu[Floor[Prime[n]/2]], {n, 105}] (* Jon Maiga, Jan 06 2019 *)
  • PARI
    a(n) = omega(prime(n)\2); \\ Michel Marcus, Jan 06 2019

Formula

a(n) = A001221(floor(A000040(n)/2)). - Jon Maiga, Jan 06 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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