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%I #14 May 07 2023 01:11:18
%S 13,15,19,43,46,49,53,60,64,66,71,78,100,102,107,108,114,134,138,139,
%T 140,158,162,170,171,173,177,178,185,191,196,230,240,254,271,290,304,
%U 314,322,360,368,395,396,402,407,416,437,439,440,443,448,465,468,472
%N Positions where Pi and the Golden Ratio have a common decimal digit.
%t With[{nn=1000},Flatten[Position[Thread[{RealDigits[GoldenRatio,10,nn][[1]],RealDigits[Pi,10,nn][[1]]}],_?(#[[1]]==#[[2]]&),{1},Heads-> False]]]
%o (Python)
%o from sympy import S
%o digits = 1000
%o pi, phi = str(S.Pi.n(digits+3)), str(S.GoldenRatio.n(digits+3))
%o print([k for k in range(2, digits+1) if pi[k] == phi[k]]) # _Michael S. Branicky_, May 06 2023
%Y Cf. A052055, A257494.
%K nonn,base
%O 1,1
%A _Harvey P. Dale_, Apr 26 2015
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