A128050 Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.

19, 5, 22, 10, 34, 55, 35, 188, 131, 174, 137, 98, 90, 27, 102, 111, 166, 1, 150, 217, 479, 44, 25, 13, 81, 458, 1242, 744, 563, 96, 1602, 186, 97, 995, 259, 939, 1999, 1204, 641, 1191, 43, 833, 1682, 2833, 2708, 188, 647, 130, 62, 734, 2337, 1106, 307, 1156, 2532

Offset: 1

Author

Gregory Allen, Feb 13 2007

Keywords

• base
• nonn

Examples

			Golden ratio phi = 1.6180339887498948482045868343656381177... (see A001622).
First occurrence of prime(1) = 2 is at the 19th digit after the decimal point, hence a(1) = 19.
First occurrence of prime(5) = 11 starts at the 34th digit after the decimal point, hence a(5) = 34.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001622, A037024, A014777.

Programs

Magma

k:=3000; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-1 + (Sqrt(elt)+1) / elt))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* Klaus Brockhaus, Feb 15 2007 */

Mathematica

Module[{p = Rest[First[RealDigits[GoldenRatio, 10, 10^4]]], n = 0, a}, Reap[While[(a = SequencePosition[p, IntegerDigits[Prime[++n]], 1]) != {}, Sow[a[[1, 1]]]]][[2, 1]]] (* Paolo Xausa, Aug 01 2024 *)

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 15 2007