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A337296
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Number whose sum and product of ternary representation digits are equal.
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1
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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
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OFFSET
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1,3
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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8 is a term since in base 3 the representation of 8 is 22 and 2 + 2 = 2 * 2.
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(m) = my(d=digits(m, 3)); vecsum(d) == vecprod(d); \\ Michel Marcus, Aug 22 2020
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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