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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

Table of n, a(n) for n=0..5.

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: A007248 A117431 A159504 * 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 May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)