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A266002 Positions in Pi, e, and the Golden Ratio indicate a common digit.

%I A266002 #18 Jan 02 2022 09:48:07
%S A266002 13,100,170,396,500,596,607,694,825,828,841,941,1283,1292,1385,1595,
%T A266002 1706,1743,1906,2021,2061,2154,2258,2303,2360,2368,2508,2547,2558,
%U A266002 2711,2725,2792,2833,2858,3037,3052,3281,3310,3430,3498,3519,3592,3652,3710,3868
%N A266002 Positions in Pi, e, and the Golden Ratio indicate a common digit.
%H A266002 Harvey P. Dale, <a href="/A266002/b266002.txt">Table of n, a(n) for n = 1..10000</a>
%e A266002 The 100th digit of Pi = the 100th digit of e = the 100th digit of the Golden Ratio = 7.
%t A266002 Module[{nn=10000,pid,ed,grd},pid=RealDigits[Pi,10,nn][[1]];ed= RealDigits[ E,10,nn][[1]];grd=RealDigits[GoldenRatio,10,nn][[1]];Flatten[ Position[ Transpose[{pid,ed,grd}],{x_,x_,x_}]]]
%o A266002 (Python 3.x)
%o A266002 from sympy import *
%o A266002 #pi, E, phi
%o A266002 pi_const = str(N(pi, 10000))
%o A266002 e_const = str(N(E, 10000))
%o A266002 phi_const = str(S.GoldenRatio.n(10000))
%o A266002 for x in range(10000):
%o A266002     if pi_const[x] == e_const[x]:
%o A266002         if e_const[x] == phi_const[x]:
%o A266002             print(x)
%o A266002 # _Glen Gilchrist_, Jan 02 2022
%Y A266002 Cf. A000796, A001113, A001622, A257492, A257494.
%K A266002 nonn,base
%O A266002 1,1
%A A266002 _Harvey P. Dale_, Dec 19 2015