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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

%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.

%C The next such number is greater than 10^6.

%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 produces all 3-digit Phithy numbers

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

%K base,more,nonn

%O 0,2

%A _Colin Rose_, Mar 14 2006

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Last modified February 18 15:04 EST 2020. Contains 332019 sequences. (Running on oeis4.)