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Irregular triangle read by rows in which row n lists algebraic prime factors of the repunit (10^n - 1)/9 (A002275(n)).
5

%I #17 May 11 2024 09:30:50

%S 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,

%T 239,4649,3,37,41,271,11,73,101,137,1,3,7,11,13,37,333667,1,11,41,101,

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

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

%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 1;

%e 1;

%e 11;

%e 1;

%e 3,11,37;

%e 1;

%e 11,101;

%e 3,37;

%e 11,41,271;

%e ...

%t 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 *)

%Y Cf. A002275, A102380, A204845.

%K nonn,tabf

%O 1,4

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

%E More terms from _Amiram Eldar_, May 11 2024