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

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

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

• nonn
• tabl

Comments

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;

Examples

			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;
  ...
		

Crossrefs

Cf. A001747, A079951, A079952, A079953.

Programs

Maple

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

PARI

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

Formula

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