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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

%I

%S 1,20,63,104,7499430,9228401

%N 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.

%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 single digit in golden ratio phi is 1.

%e Number 20 is a term because the 20th pair of digits in phi is 20.

%e (cf. phi = 1.6180339887498948482045868343656381177203...)

%t 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

%o (Python)

%o from sympy import S

%o def aupto(nn):

%o mm = len(str(nn))

%o phistr = str(S.GoldenRatio.n(nn*mm+1)).replace(".", "")[:-1]

%o for n in range(1, nn+1):

%o nstr = str(n)

%o m = len(nstr)

%o if phistr[(n-1)*m:n*m] == nstr: print(n, end=", ")

%o aupto(10**5) # _Michael S. Branicky_, Jan 20 2021

%Y Cf. A001622, A109513, A109514, A117431.

%K nonn,base,hard,more,changed

%O 0,2

%A _Colin Rose_, Mar 14 2006

%E a(4)-a(5) from _Michael S. Branicky_, Jan 21 2021

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Last modified January 21 14:44 EST 2021. Contains 340351 sequences. (Running on oeis4.)