This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337296 #16 Oct 16 2023 01:47:43
%S A337296 0,1,2,8,134,152,158,160,206,212,214,230,232,238,265760,265814,265832,
%T A337296 265838,265840,265976,265994,266000,266002,266048,266054,266056,
%U A337296 266072,266074,266080,266462,266480,266486,266488,266534,266540,266542,266558,266560,266566
%N A337296 Number whose sum and product of ternary representation digits are equal.
%C A337296 In ternary representation all the terms except 0 are zeroless (A032924).
%C A337296 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).
%C A337296 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, ...
%H A337296 Amiram Eldar, <a href="/A337296/b337296.txt">Table of n, a(n) for n = 1..10000</a>
%e A337296 8 is a term since in base 3 the representation of 8 is 22 and 2 + 2 = 2 * 2.
%t A337296 Select[Range[0, 266566], Times @@ (d = IntegerDigits[#, 3]) == Plus @@ d &]
%t A337296 (* or *)
%t A337296 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 *)
%o A337296 (PARI) isok(m) = my(d=digits(m,3)); vecsum(d) == vecprod(d); \\ _Michel Marcus_, Aug 22 2020
%Y A337296 The ternary version of A034710.
%Y A337296 Cf. A000325, A032924.
%K A337296 nonn,base
%O A337296 1,3
%A A337296 _Amiram Eldar_, Aug 21 2020