A169868 -id:A169868 - cp's OEIS frontend

A068432 Expansion of golden ratio (1 + sqrt(5))/2 in base 2.

1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0

Offset: 1

Benoit Cloitre, Mar 09 2002

Differs from A004555 in the 2nd digit. - R. J. Mathar, Dec 15 2008

			1.1001111000110111011110011011100101...

Cf. A001622, A004555, A004714, A169868.

RealDigits[ (1+Sqrt[5])/2, 2, 1000][[1]]

concat(binary((1+sqrt(5))/2)) \\ Michel Marcus, Dec 14 2017

a(n) = floor(quadgen(5)*2^(n-1))%2 \\ Chittaranjan Pardeshi, Feb 06 2023

A004714 Positions of ones in binary expansion of the reciprocal of the golden ratio (0.618...).

Original entry on oeis.org

1, 4, 5, 6, 7, 11, 12, 14, 15, 16, 18, 19, 20, 21, 24, 25, 27, 28, 29, 32, 34, 35, 36, 37, 38, 39, 40, 42, 45, 47, 50, 51, 52, 53, 54, 60, 62, 64, 65, 66, 67, 68, 71, 72, 73, 76, 77, 78, 81, 82, 90, 91, 98, 100, 101, 102

Offset: 1

Simon Plouffe

nonn

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A068432, A169868.

Position[RealDigits[1/GoldenRatio,2,150][[1]],1]//Flatten (* Harvey P. Dale, Jul 30 2025 *)

cp's OEIS Frontend

A068432 Expansion of golden ratio (1 + sqrt(5))/2 in base 2.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI