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A117431 String n is at position n in decimal digits of golden ratio (phi). 1

%I

%S 1,20,62,9956

%N String n is at position n in decimal digits of golden ratio (phi).

%C The next such number is greater than 10^7. Not only does number 20 occur at the 20th digit, but it occurs again as the 20th pair of digits (cf. A117432).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">The Golden Ratio</a>

%e 1 is a term because the first digit in the golden ratio phi is 1. (phi = 1.6180339887498948482045 ...)

%t StringFinder[m_] := Module[{cc = 10^m + m, sol, aa}, sol = Partition[RealDigits[(1+Sqrt[5])/2, 10, cc] // First, m, 1]; Do[aa = FromDigits[sol[[i]]]; If[aa==i, Print[{i, aa}]], {i,Length[sol]}];] Example: StringFinder[2] produces all 2-digit members of the sequence.

%Y Cf. A001622, A057679, A117432.

%K base,more,nonn

%O 1,2

%A _Colin Rose_, Mar 14 2006

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Last modified June 23 13:26 EDT 2017. Contains 288665 sequences.