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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Aug 21 2020
STATUS
approved