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 A117432 Let n be an integer consisting of m digits. Then n is a Phithy number if the n-th m-tuple in the decimal digits of golden ratio phi is string n. 1
 1, 20, 63, 104, 7499430, 9228401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Eric Weisstein's World of Mathematics, The Golden Ratio EXAMPLE 1 is a term because the first single digit in golden ratio phi is 1. Number 20 is a term because the 20th pair of digits in phi is 20. (cf. phi = 1.6180339887498948482045868343656381177203...) MATHEMATICA PhithyNumbers[m_] := Module[{cc = m(10^m)+m, sol, aa}, sol = Partition[RealDigits[GoldenRatio, 10, cc] // First, m]; Do[aa = FromDigits[sol[[i]]]; If[aa==i, Print[{i, aa}]], {i, Length[sol]}]; ] Example: PhithyNumbers[3] produces all 3-digit Phithy numbers PROG (Python) from sympy import S def aupto(nn): mm = len(str(nn)) phistr = str(S.GoldenRatio.n(nn*mm+1)).replace(".", "")[:-1] for n in range(1, nn+1): nstr = str(n) m = len(nstr) if phistr[(n-1)*m:n*m] == nstr: print(n, end=", ") aupto(10**5) # Michael S. Branicky, Jan 20 2021 CROSSREFS Cf. A001622, A109513, A109514, A117431. Sequence in context: A117431 A159504 A182468 * A033577 A262486 A187156 Adjacent sequences: A117429 A117430 A117431 * A117433 A117434 A117435 KEYWORD nonn,base,hard,more AUTHOR Colin Rose, Mar 14 2006 EXTENSIONS a(4)-a(5) from Michael S. Branicky, Jan 21 2021 STATUS approved

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