A174433 Triangle read by rows: T(n,k) = prime(n) mod A001223(k), where A001223 are differences between consecutive primes.

0, 0, 1, 0, 1, 1, 0, 1, 1, 3, 0, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 3, 1, 3, 0, 1, 1, 3, 1, 3, 1, 3, 5, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 28 2010

Keywords

• nonn
• tabl

Comments

The first prime gap is 3-2=1, so the first column is T(n,1)=0. The second and third prime gaps are 5-3=2 and 7-5=2, and since all primes > 2 are odd, T(n,2) = T(n,3) = 1.

Examples

			Triangle begins:
  0;
  0,1;
  0,1,1;
  0,1,1,3;
  0,1,1,3,1;
		

Crossrefs

Cf. A000040.

Programs

Maple

A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end proc:
A174433 := proc(n,k) ithprime(n) mod A001223(k) ; end proc:
seq(seq(A174433(n,k),k=1..n),n=1..14) ;