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

1,1

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.

Links

Table of n, a(n) for n=1..31.

Example

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

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 *)

Crossrefs

Cf. A002283, A074992, A237424.

Sequence in context: A292449 A292739 A266022 * A147829 A116274 A116286

Adjacent sequences: A284688 A284689 A284690 * A284692 A284693 A284694

Keyword

nonn,base

Author

Ahmad J. Masad, Apr 01 2017

Extensions

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

Status

approved