A173655 Triangle read by rows: T(n,k) = prime(n) mod prime(k), 0 < k <= n.

0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 1, 4, 0, 1, 1, 3, 6, 2, 0, 1, 2, 2, 3, 6, 4, 0, 1, 1, 4, 5, 8, 6, 2, 0, 1, 2, 3, 2, 1, 10, 6, 4, 0, 1, 2, 4, 1, 7, 3, 12, 10, 6, 0, 1, 1, 1, 3, 9, 5, 14, 12, 8, 2, 0, 1, 1, 2, 2, 4, 11, 3, 18, 14, 8, 6, 0, 1, 2, 1, 6, 8, 2, 7, 3, 18, 12, 10, 4, 0

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 24 2010

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
  0;
  1, 0;
  1, 2, 0;
  1, 1, 2, 0;
  1, 2, 1, 4, 0;
  1, 1, 3, 6, 2,  0;
  1, 2, 2, 3, 6,  4,  0;
  1, 1, 4, 5, 8,  6,  2,  0;
  1, 2, 3, 2, 1, 10,  6,  4, 0;
  1, 2, 4, 1, 7,  3, 12, 10, 6, 0;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A001223 (2nd diagonal), A033955 (row sums), A102647 (row products excluding 0's), A031131 (3rd diagonal after first 3 terms).

Cf. A172662, A174497, A174947, A174996, A175620.

Programs

Magma

A173655:= func< n,k | NthPrime(n) mod NthPrime(k) >;
[A173655(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2024

Maple

A173655 := proc(n,k) ithprime(n) mod ithprime(k) ;end proc:
seq(seq(A173655(n,k),k=1..n),n=1..20) ; # R. J. Mathar, Nov 24 2010

Mathematica

Flatten[Table[Mod[Prime[n], Prime[Range[n]]], {n, 15}]]

PARI

forprime(p=2,40,forprime(q=2,p,print1(p%q", "))) \\ Charles R Greathouse IV, Dec 21 2011

SageMath

def A173655(n,k): return nth_prime(n)%nth_prime(k)
flatten([[A173655(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Apr 10 2024