A176904 A coding sequence of binary based integers using powers of {2,3} for {0,1}.

3, 8, 24, 64, 7776, 20736, 13824, 36864, 45349632, 120932352, 80621568, 214990848, 322486272, 859963392, 573308928, 1528823808, 1028294561267712, 2742118830047232, 1828079220031488, 4874877920083968, 7312316880125952

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