A204845 Irregular triangle read by rows in which row n lists primitive prime factors of the repunit (10^n - 1)/9 (A002275(n)).

1, 11, 3, 37, 101, 41, 271, 7, 13, 239, 4649, 73, 137, 333667, 9091, 21649, 513239, 9901, 53, 79, 265371653, 909091, 31, 2906161, 17, 5882353, 2071723, 5363222357, 19, 52579, 1111111111111111111, 3541, 27961, 43, 1933, 10838689, 23, 4093, 8779, 11111111111111111111111

Offset

1,2

Links

Ray Chandler, Rows n = 1..322, flattened (first 60 rows from Alois P. Heinz)

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

Example

Triangle begins:
1
11
3 37
101
41 271
7 13
239 4649
73 137
333667
9091
...

Maple

with(numtheory):
S:= proc(n) option remember;
      `if`(n=1, {1}, S(n-1) union factorset ((10^n-1)/9))
    end:
T:= n-> sort([(S(n) minus `if`(n=1, {}, S(n-1)))[]])[]:
seq(T(n), n=1..30);  # Alois P. Heinz, Feb 17 2012

Mathematica

S[n_] := S[n] = If[n==1, {1}, S[n-1] ~Union~ FactorInteger[(10^n-1)/9][[ All, 1]]]; T[n_] := Sort[S[n] ~Complement~ If[n==1, {}, S[n-1]]]; Table[ T[n], {n, 1, 30}] // Flatten (* Jean-François Alcover, Mar 13 2017, after Alois P. Heinz *)

Crossrefs

Cf. A002275, A102380, A204846, A204847, A204848.

Sequence in context: A298256 A298927 A102380 * A260597 A147555 A157883

Adjacent sequences: A204842 A204843 A204844 * A204846 A204847 A204848

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 19 2012

Extensions

More terms from Alois P. Heinz, Feb 17 2012

Status

approved