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

1,3

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, ...

Links

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

Example

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

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 *)

Prog

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

Crossrefs

The ternary version of A034710.

Cf. A000325, A032924.

Sequence in context: A184945 A058343 A267407 * A111827 A045330 A193203

Adjacent sequences: A337293 A337294 A337295 * A337297 A337298 A337299

Keyword

nonn,base

Author

Amiram Eldar, Aug 21 2020

Status

approved