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 A176904 A coding sequence of binary based integers using powers of {2,3} for {0,1}. 0
 3, 8, 24, 64, 7776, 20736, 13824, 36864, 45349632, 120932352, 80621568, 214990848, 322486272, 859963392, 573308928, 1528823808, 1028294561267712, 2742118830047232, 1828079220031488, 4874877920083968, 7312316880125952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Based on a 2 for zero and three for one substitution, this apparently unique Goedelization of the binary numbers uses the Fibonacci sequence to make the digit ordering unique. LINKS Table of n, a(n) for n=0..20. FORMULA The sum of digits is weighted by the Fibonacci sequence to give: a(n)=6^(sum[n]*Fibonacci[n])*2^(Count[n,2]+PosititionSum[n,2])*3^(Count[n,3]+PosititionSum[n,3])/3 MATHEMATICA Table[6^(Sum[Table[((Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]][[ m]]*Fibonacci[m], {m, 1, Length[ Table[((Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]]]}])*2^(-(Count[ Table[((IntegerDigits[n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]], 2] + Apply[Plus, Flatten[ Position[Table[((Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]], 2]]]))*3^(-( Count[Table[((IntegerDigits[n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[ n]], 3] + Apply[Plus, Flatten[Position[Table[(( Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, { n, 0, 50}][[n]], 3]]]))/3, {n, 1, 51}] CROSSREFS Sequence in context: A096001 A080097 A096886 * A056332 A091588 A297219 Adjacent sequences: A176901 A176902 A176903 * A176905 A176906 A176907 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Apr 28 2010 STATUS approved

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Last modified June 10 13:58 EDT 2023. Contains 363205 sequences. (Running on oeis4.)