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

1,2

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.

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

Example

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.

Crossrefs

Cf. A001622, A055778, A105424, A130600.

Sequence in context: A084456 A283708 A284484 * A283648 A284483 A283707

Adjacent sequences: A130598 A130599 A130600 * A130602 A130603 A130604

Keyword

nonn,base

Author

Casey Mongoven, Aug 06 2007

Status

approved