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Numbers of the form (10^c-1)*the product any two (not necessarily distinct) terms of A074992.
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%I #26 Oct 03 2017 10:30:00

%S 9,99,333,999,3663,9999,12321,30303,36963,99999,135531,333333,369963,

%T 999999,1121211,1367631,3003003,3363633,3699963,9999999,12333321,

%U 13688631,33033033,33666633,36999963,99999999,102030201,111111111,124454421,136898631,300030003

%N Numbers of the form (10^c-1)*the product any two (not necessarily distinct) terms of A074992.

%C Conjecture 1: all terms are palindromic in base 10.

%C Conjecture 2: the sequence A074992 is the maximally dense sequence with this palindromic products property.

%e a(3) = 37*9 = 333, with respect to strictly increasing ordering.

%t f[n_] := f[n] = (10^(2 n) + 10^n + 1)/3; c[n_] := 10^n - 1; mx = 10^10; i=1; Union@ Reap[ While[c[i] <= mx, j=0; While[c[i] f[j] <= mx, k=0; While[k <= j && (v = c[i] f[j] f[k]) <= mx, Sow@v; k++]; j++]; i++]][[2, 1]] (* _Giovanni Resta_, Apr 01 2017 *)

%Y Cf. A002283, A074992, A237424.

%K nonn,base

%O 1,1

%A _Ahmad J. Masad_, Apr 01 2017

%E a(13)-a(31) from _Giovanni Resta_, Apr 01 2017