A362058 The location of the first occurrence of n in the decimal expansion of phi (the golden ratio, 1.6180339887...).

4, 0, 19, 5, 11, 22, 1, 10, 3, 7, 231, 34, 121, 55, 254, 366, 0, 35, 2, 188, 19, 54, 62, 131, 78, 213, 67, 63, 51, 174, 40, 137, 181, 5, 26, 56, 28, 98, 32, 6, 105, 90, 347, 27, 58, 21, 70, 102, 15, 11, 214, 394, 66, 111, 57, 768, 30, 48, 22, 166, 68, 1, 50

Offset

0,1

Comments

Locations in the expansion of phi are numbered 0 for the digit before the decimal point, 1 for the first digit after the decimal point, and so on.

Links

Table of n, a(n) for n=0..62.

Formula

a(n) = A088577(n) - 1.

Example

The first occurrence of 0 in phi occurs 4 places after the decimal point, so a(0)=4; 5 first occurs 22 places after the decimal point, so a(5)=22; 10 first occurs 231 places after the decimal point so a(10)=231.

Mathematica

Table[-1 + SequencePosition[#, IntegerDigits@ n][[1, 1]], {n, 0, 50}] &@ First@ RealDigits@ N[GoldenRatio, 10^4]

Crossrefs

Cf. A001622 (phi)

Cf. A088577 (1-based locations).

Cf. A078197 (for e), A176341 (for Pi), A014777 (for Pi but different indexing).

Sequence in context: A058348 A184946 A351615 * A085618 A263626 A282579

Adjacent sequences: A362055 A362056 A362057 * A362059 A362060 A362061

Keyword

nonn,base

Author

James C. McMahon, Apr 06 2023

Status

approved