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A130600
Integers written in base phi, with the "decimal point" omitted.
10
1, 1001, 10001, 10101, 10001001, 10100001, 100000001, 100010001, 100100101, 101000101, 101010101, 100000101001, 100010001001, 100100001001, 100101001001, 101000100001, 101010000001, 1000000000001, 1000001000001
OFFSET
1,2
COMMENTS
This is the "greedy" or "minimal" representation (see also A130601).
LINKS
Casey Mongoven and T. D. Noe, Table of n, a(n) for n = 1..1000
EXAMPLE
If the decimal point were included, the sequence would read 1., 10.01, 100.01, 101.01, 1000.1001, 1010.0001, 10000.0001, 10001.0001, 10010.0101, 10100.0101, 10101.0101, ... Unfortunately these are not integers.
Examples: a(2)=1001 because phi^1+phi^-2 = 2, a(3) = 10001 because phi^2+phi^-2 = 3, a(4) = 10101 because phi^2+phi^0+phi^-2 = 4.
MATHEMATICA
nn = 100; len = 2*Ceiling[Log[GoldenRatio, nn]]; Table[d = RealDigits[n, GoldenRatio, len]; last1 = Position[d[[1]], 1][[-1, 1]]; FromDigits[Take[d[[1]], last1]], {n, nn}] (* T. D. Noe, May 20 2011 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Casey Mongoven, Aug 06 2007
STATUS
approved