A079951 -id:A079951 - cp's OEIS frontend

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

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

Reinhard Zumkeller, Jan 19 2003

nonn

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]

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

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

Table[PrimePi[Prime[n]/2], {n, 75}] (* Michael De Vlieger, Sep 20 2017 *)

a(n) = primepi(prime(n)/2); \\ Michel Marcus, Sep 20 2017

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).

New name from Peter Munn, Sep 18 2017

A079950 Triangle of n-th prime modulo twice primes less n-th prime.

Original entry on oeis.org

2, 3, 3, 1, 5, 5, 3, 1, 7, 7, 3, 5, 1, 11, 11, 1, 1, 3, 13, 13, 13, 1, 5, 7, 3, 17, 17, 17, 3, 1, 9, 5, 19, 19, 19, 19, 3, 5, 3, 9, 1, 23, 23, 23, 23, 1, 5, 9, 1, 7, 3, 29, 29, 29, 29, 3, 1, 1, 3, 9, 5, 31, 31, 31, 31, 31, 1, 1, 7, 9, 15, 11, 3, 37, 37, 37, 37, 37, 1, 5, 1, 13, 19, 15, 7, 3, 41

Offset: 1

Reinhard Zumkeller, Jan 19 2003

The right border of the triangle are the primes: T(n,n)=A000040(n); T(n,1)=A039702(n), T(n,2)=A039704(n) for n>1, T(n,3)=A007652(n) for n>2, T(n,4)=A039712(n) for n>3;

			Triangle begins:
  2;
  3, 3;
  1, 5, 5;
  3, 1, 7,  7;
  3, 5, 1, 11, 11;
  1, 1, 3, 13, 13, 13;
  1, 5, 7,  3, 17, 17, 17;
  ...

Cf. A001747, A079951, A079952, A079953.

A079950 := proc(n,k)
    modp(ithprime(n),2*ithprime(k)) ;
end proc:
seq(seq(A079950(n,k),k=1..n),n=1..12) ; # R. J. Mathar, Sep 28 2017

T(n,k) = prime(n) % (2*prime(k));
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, Sep 21 2017

T(n, k) = prime(n) mod 2*prime(k), 1<=k<=n.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions