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 A117431 String n is at position n in decimal digits of golden ratio (phi). 1
 1, 20, 62, 9956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS Eric Weisstein's World of Mathematics, The Golden Ratio EXAMPLE 1 is a term because the first digit in the golden ratio phi is 1. (phi = 1.6180339887498948482045 ...) MATHEMATICA 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. *) PROG (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 CROSSREFS Cf. A001622, A057679, A117432. Sequence in context: A105092 A112144 A007248 * A159504 A182468 A117432 Adjacent sequences: A117428 A117429 A117430 * A117432 A117433 A117434 KEYWORD nonn,base,hard,more AUTHOR Colin Rose, Mar 14 2006 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)