login
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
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.
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
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Apr 28 2010
STATUS
approved