A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).

1, 0, 2, 0, 1, 4, 0, 0, 1, 6, 0, 1, 0, 3, 10, 0, 0, 2, 5, 1, 12, 0, 1, 1, 2, 5, 3, 16, 0, 0, 3, 4, 7, 5, 1, 18, 0, 1, 2, 1, 0, 9, 5, 3, 22, 0, 1, 3, 0, 6, 2, 11, 9, 5, 28, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 30, 0, 0, 1, 1, 3, 10, 2, 17, 13, 7, 5, 36, 0, 1, 0, 5, 7, 1, 6, 2, 17, 11, 9, 3, 40, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 42

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 02 2010

Keywords

• nonn
• tabl

Examples

			The triangle starts in row n=0 with columns 1<=k<= n as:
  1;
  0, 2;
  0, 1, 4;
  0, 0, 1, 6;
  0, 1, 0, 3, 10;
  0, 0, 2, 5,  1, 12;
  0, 1, 1, 2,  5,  3, 16;
  0, 0, 3, 4,  7,  5,  1, 18;
  0, 1, 2, 1,  0,  9,  5,  3, 22;
  0, 1, 3, 0,  6,  2, 11,  9,  5, 28;
		

Links

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

Crossrefs

Cf. A006093, A173655, A173662, A174428, A174947, A175620, A176066, A177226.

Programs

Magma

[(NthPrime(n)-1) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 12 2024

Mathematica

Flatten[Table[Mod[Prime[n]-1,Prime[k]],{n,15},{k,n}]]  (* Harvey P. Dale, Apr 23 2011 *)

SageMath

flatten([[(nth_prime(n)-1)%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 12 2024