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A117431
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String n is at position n in decimal digits of golden ratio (phi).
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1
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..4.
Eric Weisstein's World of Mathematics, The Golden Ratio
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EXAMPLE
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1 is a term because the first digit in the golden ratio phi is 1. (phi = 1.6180339887498948482045 ...)
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MATHEMATICA
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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. *)
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PROG
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(Python)
from sympy import S
def aupto(nn):
phistr = str(S.GoldenRatio.n(nn+len(str(nn))+1)).replace(".", "")[:-1]
for n in range(1, nn+1):
nstr = str(n)
if phistr[n-1:n-1+len(nstr)] == nstr: print(n, end=", ")
aupto(10**5) # Michael S. Branicky, Jan 20 2021
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CROSSREFS
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Cf. A001622, A057679, A117432.
Sequence in context: A105092 A112144 A007248 * A159504 A182468 A117432
Adjacent sequences: A117428 A117429 A117430 * A117432 A117433 A117434
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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Colin Rose, Mar 14 2006
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STATUS
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approved
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