A004714 -id:A004714 - 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

A164629 Expansion of phi (golden ratio) in base 5.

Original entry on oeis.org

1, 3, 0, 2, 1, 1, 1, 3, 4, 2, 3, 0, 4, 1, 2, 0, 2, 4, 2, 2, 3, 1, 4, 4, 3, 1, 1, 4, 0, 2, 0, 4, 0, 2, 1, 2, 1, 1, 1, 0, 3, 3, 1, 3, 3, 0, 4, 0, 0, 4, 0, 2, 4, 1, 0, 2, 2, 3, 0, 1, 1, 0, 4, 3, 4, 2, 2, 2, 1, 4, 4, 2, 1, 2, 1, 1, 4, 4, 3, 2, 2, 2, 1, 0, 3, 1, 2, 4, 1, 0

Offset: 1

Keith Rarick, Dan McCandless (kr(AT)xph.us), Aug 18 2009

Cf. A001622, A004714.

RealDigits[(1 + Sqrt[5])/2, 5, 90]
RealDigits[GoldenRatio,5,120][[1]] (* Harvey P. Dale, Jan 19 2021 *)

default(realprecision, 1000); x=(1+sqrt(5))/2;
for(n=1, 100, d=floor(x); x=(x-d)*5; print1(d, ", ")); \\ Jinyuan Wang, Mar 21 2020

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

A169868 Positions of zeros in binary expansion of the reciprocal of the golden ratio (0.618...).

Original entry on oeis.org

2, 3, 8, 9, 10, 13, 17, 22, 23, 26, 30, 31, 33, 41, 43, 44, 46, 48, 49, 55, 56, 57, 58, 59, 61, 63, 69, 70, 74, 75, 79, 80, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 99, 103, 104, 108, 111, 115, 116, 118, 119, 120, 121, 122, 125, 127, 128, 129, 130, 131, 133, 134, 135

Offset: 1

N. J. A. Sloane, Jul 04 2010

nonn

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

Cf. A068432, A004714.

Position[RealDigits[1/GoldenRatio,2,150][[1]],0]//Flatten (* Harvey P. Dale, Aug 08 2017 *)

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

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A164629 Expansion of phi (golden ratio) in base 5.

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A169868 Positions of zeros in binary expansion of the reciprocal of the golden ratio (0.618...).

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