A204846 Irregular triangle read by rows in which row n lists algebraic prime factors of the repunit (10^n - 1)/9 (A002275(n)).

1, 1, 1, 11, 1, 3, 11, 37, 1, 11, 101, 3, 37, 11, 41, 271, 1, 3, 7, 11, 13, 37, 101, 1, 11, 239, 4649, 3, 37, 41, 271, 11, 73, 101, 137, 1, 3, 7, 11, 13, 37, 333667, 1, 11, 41, 101, 271, 9091, 3, 37, 239, 4649, 11, 21649, 513239, 1, 3, 7, 11, 13, 37, 73, 101, 137, 9901, 41, 271

Offset: 1

Author

N. J. A. Sloane, Jan 19 2012

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  1;
  1;
  11;
  1;
  3,11,37;
  1;
  11,101;
  3,37;
  11,41,271;
  ...
		

Links

• Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28.

Crossrefs

Cf. A002275, A102380, A204845.

Programs

Mathematica

rows[nmax_] := Module[{prim = {1}, r = {{1}}, p, c}, Do[p = FactorInteger[(10^n - 1)/9][[;; , 1]]; c = Complement[p, Complement[p, prim]]; If[c == {}, c = {1}]; AppendTo[r, c]; prim = Union[prim, p], {n, 2, nmax}]; r]; rows[25] // Flatten (* Amiram Eldar, May 11 2024 *)

Extensions

More terms from Amiram Eldar, May 11 2024