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

1,1

Links

Nathaniel Johnston, Rows 1..100, flattened

Example

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

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 *)

Crossrefs

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

Sequence in context: A178766 A362778 A362779 * A082011 A101044 A077321

Adjacent sequences: A077313 A077314 A077315 * A077317 A077318 A077319

Keyword

nonn,easy,tabl

Author

Amarnath Murthy, Nov 04 2002

Extensions

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

Status

approved