A130600 Integers written in base phi, with the "decimal point" omitted.

1, 1001, 10001, 10101, 10001001, 10100001, 100000001, 100010001, 100100101, 101000101, 101010101, 100000101001, 100010001001, 100100001001, 100101001001, 101000100001, 101010000001, 1000000000001, 1000001000001

Offset: 1

Author

Casey Mongoven, Aug 06 2007

Keywords

• nonn
• base

Comments

This is the "greedy" or "minimal" representation (see also A130601).

Examples

			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.
		

Links

• Casey Mongoven and T. D. Noe, Table of n, a(n) for n = 1..1000
• Casey Mongoven, Music based on this sequence
• Ron Knott, Integers written in base phi

Crossrefs

Cf. A001622, A055778, A105424, A130601.

Programs

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 *)