A362058 Contributions to OEIS

 

A362058 The location of the first occurrence of n in the decimal expansion of phi (the golden ratio, 1.6180339887...). 0 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 (list; graph; refs; listen; history; edit; text; internal format) 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