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A117432
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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.
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1
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..5.
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 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...)
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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Cf. A001622, A109513, A109514, A117431.
Sequence in context: A117431 A159504 A182468 * A033577 A262486 A187156
Adjacent sequences: A117429 A117430 A117431 * A117433 A117434 A117435
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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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EXTENSIONS
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a(4)-a(5) from Michael S. Branicky, Jan 21 2021
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STATUS
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approved
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