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

1,10

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.

Links

Table of n, a(n) for n=1..105.

Example

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

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) ;

Crossrefs

Cf. A000040.

Sequence in context: A350829 A249767 A341411 * A174624 A029358 A088512

Adjacent sequences: A174430 A174431 A174432 * A174434 A174435 A174436

Keyword

nonn,tabl

Author

Juri-Stepan Gerasimov, Nov 28 2010

Status

approved