A077316 Triangle read by rows: T(n,k) is the k-th prime = 1 (mod n).

2, 3, 5, 7, 13, 19, 5, 13, 17, 29, 11, 31, 41, 61, 71, 7, 13, 19, 31, 37, 43, 29, 43, 71, 113, 127, 197, 211, 17, 41, 73, 89, 97, 113, 137, 193, 19, 37, 73, 109, 127, 163, 181, 199, 271, 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 23, 67, 89, 199, 331, 353

Offset: 1

Author

Amarnath Murthy, Nov 04 2002

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
   2;
   3,  5;
   7, 13, 19;
   5, 13, 17, 29;
  11, 31, 41, 61, 71;
  ...
		

Links

• Nathaniel Johnston, Rows 1..100, flattened

Crossrefs

Cf. A034694 (first column), A077317 (main diagonal), A077318 (row sums), A077319, A093870, A193869 (row products).

Programs

Maple

Tj := proc(n,k) option remember: local j,p: if(k=0)then return 0:fi: for j from procname(n,k-1)+1 do if(isprime(n*j+1))then return j: fi: od: end: A077316 := proc(n,k) return n*Tj(n,k)+1: end: seq(seq(A077316(n,k),k=1..n),n=1..15); # Nathaniel Johnston, Sep 02 2011

Mathematica

Tj[n_, k_] := Tj[n, k] = Module[{j}, If[k == 0, Return[0]];
   For[j = Tj[n, k-1]+1, True, j++, If[PrimeQ[n*j+1], Return[j]]]];
T[n_, k_] := n*Tj[n, k]+1;
Table[Table[T[n, k], {k, 1, n}], {n, 1, 15}] // Flatten (* Jean-François Alcover, Aug 02 2022, after Nathaniel Johnston *)

Extensions

Edited and extended by Franklin T. Adams-Watters, Aug 29 2006