A130601 Integers written in base phi, with the "decimal point" omitted.

1, 111, 1101, 10101, 1011111, 1110111, 10101101, 10111101, 11011101, 11110101, 101010101, 10101111111, 10111011111, 11010110111, 11011110111, 11101110111, 11111010111, 101010101101, 101011101101, 101101101101

Offset: 1

Author

Casey Mongoven, Aug 06 2007

Keywords

• nonn
• base

Comments

The map 100 -> 011 is used to eliminate every 100 from the minimal representation (A130600).

Other sequences are possible for representing integers in base-phi with no occurrence of "00" in any terms - see links.

Examples

			Examples: a(2)=111 because phi^0+phi^-1+phi^-2 = 2, a(3) = 1101 because phi^1+phi^0+phi^-2 = 3, a(4) = 10101 because phi^2+phi^0+phi^-2 = 4.
		

Links

• Casey Mongoven, Table of n, a(n) for n = 1..55
• L. C. Eggan, C. L. Vanden Eynden, "Decimal" expansions to nonintegral bases, Am. Math. Monthly 73 (6) (1966) 576-582
• Ron Knott, Integers written in base phi
• Casey Mongoven, Music based on this sequence

Crossrefs

Cf. A001622, A055778, A105424, A130600.