A284691 Numbers of the form (10^c-1)*the product any two (not necessarily distinct) terms of A074992.

9, 99, 333, 999, 3663, 9999, 12321, 30303, 36963, 99999, 135531, 333333, 369963, 999999, 1121211, 1367631, 3003003, 3363633, 3699963, 9999999, 12333321, 13688631, 33033033, 33666633, 36999963, 99999999, 102030201, 111111111, 124454421, 136898631, 300030003

Offset: 1

Author

Ahmad J. Masad, Apr 01 2017

Keywords

• nonn
• base

Comments

Conjecture 1: all terms are palindromic in base 10.

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

Examples

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

Crossrefs

Cf. A002283, A074992, A237424.

Programs

Mathematica

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 *)

Extensions

a(13)-a(31) from Giovanni Resta, Apr 01 2017