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

Author

James C. McMahon, Apr 06 2023

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

Cf. A001622 (phi)

Cf. A088577 (1-based locations).

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

Programs

Mathematica

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

Formula

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