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A176341 a(n) = the location of the first appearance of the decimal expansion of n in the decimal expansion of Pi. 17


%S 32,1,6,0,2,4,7,13,11,5,49,94,148,110,1,3,40,95,424,37,53,93,135,16,

%T 292,89,6,28,33,186,64,0,15,24,86,9,285,46,17,43,70,2,92,23,59,60,19,

%U 119,87,57,31,48,172,8,191,130,210,404,10,4,127,219,20,312,22,7,117,98,605,41

%N a(n) = the location of the first appearance of the decimal expansion of n in the decimal expansion of Pi.

%C It is unknown whether Pi is a normal number. If it is (at least in base 10) then this sequence is well defined.

%C The numbers a(n) refer to the position of the initial digit of n in the decimal expansion of Pi, where "3" is at position a(3)=0, "1" is at position a(1)=1, etc. This is also the numbering scheme used on the "Pi search page" cited among the LINKS. See A232013 for a sequence based on iterations of this one. See A032445 for a variant of the present sequence, where numbering starts at one. - _M. F. Hasler_, Nov 16 2013

%H Vincenzo Librandi, <a href="/A176341/b176341.txt">Table of n, a(n) for n = 0..1000</a>

%H Author?, <a href="http://www.angio.net/pi/piquery">Search within first 200,000,000 digits of pi</a>

%H Michael D. Huberty, Ko Hayashi & Chia Vang, <a href="http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html">First 100,000 digits of pi</a>

%H Simon Plouffe, <a href="http://oldweb.cecm.sfu.ca/projects/ISC/data/pi.html">First 50,000,000 digits of pi</a>

%F a(n) = A032445(n)-1. - _M. F. Hasler_, Nov 16 2013

%t p=ToString[FromDigits[RealDigits[N[Pi, 10^4]][[1]]]]; Do[Print[StringPosition[p, ToString[n]][[1]][[1]] - 1], {n, 0, 100}] (* _Vincenzo Librandi_, Apr 17 2017 *)

%t With[{pid=RealDigits[Pi,10,800][[1]]},Flatten[Table[ SequencePosition[ pid,IntegerDigits[n],1],{n,0,70}],1]][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 27 2019 *)

%o (Python)

%o pi = "314159265358979323846264338327950288419716939937510582097494459230..."

%o [ pi.find(str(i)) for i in range(10000) ]

%o (PARI) A176341(n)=my(L=#Str(n));n=Mod(n,10^L);for(k=L-1,9e9,Pi\.1^k-n||return(k+1-L)) \\ Make sure to use sufficient realprecision, e.g. via \p999. - _M. F. Hasler_, Nov 16 2013

%Y Cf. A000796.

%K base,nonn

%O 0,1

%A _Daniel E. Loeb_, Apr 15 2010

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Last modified August 6 15:36 EDT 2020. Contains 336252 sequences. (Running on oeis4.)