A337296 Number whose sum and product of ternary representation digits are equal.

0, 1, 2, 8, 134, 152, 158, 160, 206, 212, 214, 230, 232, 238, 265760, 265814, 265832, 265838, 265840, 265976, 265994, 266000, 266002, 266048, 266054, 266056, 266072, 266074, 266080, 266462, 266480, 266486, 266488, 266534, 266540, 266542, 266558, 266560, 266566

Offset: 1

Author

Amiram Eldar, Aug 21 2020

Keywords

• nonn
• base

Comments

In ternary representation all the terms except 0 are zeroless (A032924).

If k is the number of digits 2 of a term, then the number of digits 1 is 2^k - 2*k, and the total number of digits is thus 2^k - k (A000325).

The total number of terms with k digits 2, for k = 1, 2, ..., is binomial(2^k-k,k) = 1, 1, 10, 495, 80730, 40475358, ...

Examples

			8 is a term since in base 3 the representation of 8 is 22 and 2 + 2 = 2 * 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The ternary version of A034710.

Cf. A000325, A032924.

Programs

Mathematica

Select[Range[0, 266566], Times @@ (d = IntegerDigits[#, 3]) == Plus @@ d &]
(* or *)
f[k_] := FromDigits[#, 3] & /@ Permutations[Join[Table[1, {2^k - 2*k}], Table[2, k]]]; Flatten@ Join[{0}, Table[f[k], {k, 0, 4}]] (* Amiram Eldar, Oct 16 2023 *)

PARI

isok(m) = my(d=digits(m,3)); vecsum(d) == vecprod(d); \\ Michel Marcus, Aug 22 2020