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Irregular triangle read by rows in which row n lists primitive prime factors of the repunit (10^n - 1)/9 (A002275(n)).
6

%I #31 May 01 2017 17:47:32

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

%T 9901,53,79,265371653,909091,31,2906161,17,5882353,2071723,5363222357,

%U 19,52579,1111111111111111111,3541,27961,43,1933,10838689,23,4093,8779,11111111111111111111111

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

%H Ray Chandler, <a href="/A204845/b204845.txt">Rows n = 1..322, flattened</a> (first 60 rows from Alois P. Heinz)

%H Samuel Yates, <a href="http://www.jstor.org/stable/2689643">The Mystique of Repunits</a>, Math. Mag. 51 (1978), 22-28.

%e Triangle begins:

%e 1

%e 11

%e 3 37

%e 101

%e 41 271

%e 7 13

%e 239 4649

%e 73 137

%e 333667

%e 9091

%e ...

%p with(numtheory):

%p S:= proc(n) option remember;

%p `if`(n=1, {1}, S(n-1) union factorset ((10^n-1)/9))

%p end:

%p T:= n-> sort([(S(n) minus `if`(n=1, {}, S(n-1)))[]])[]:

%p seq(T(n), n=1..30); # _Alois P. Heinz_, Feb 17 2012

%t 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_ *)

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

%K nonn,tabf

%O 1,2

%A _N. J. A. Sloane_, Jan 19 2012

%E More terms from _Alois P. Heinz_, Feb 17 2012