

A176341


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


17



32, 1, 6, 0, 2, 4, 7, 13, 11, 5, 49, 94, 148, 110, 1, 3, 40, 95, 424, 37, 53, 93, 135, 16, 292, 89, 6, 28, 33, 186, 64, 0, 15, 24, 86, 9, 285, 46, 17, 43, 70, 2, 92, 23, 59, 60, 19, 119, 87, 57, 31, 48, 172, 8, 191, 130, 210, 404, 10, 4, 127, 219, 20, 312, 22, 7, 117, 98, 605, 41
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OFFSET

0,1


COMMENTS

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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Author?, Search within first 200,000,000 digits of pi
Michael D. Huberty, Ko Hayashi & Chia Vang, First 100,000 digits of pi
Simon Plouffe, First 50,000,000 digits of pi


FORMULA

a(n) = A032445(n)1.  M. F. Hasler, Nov 16 2013


MATHEMATICA

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 *)
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 *)


PROG

(Python)
pi = "314159265358979323846264338327950288419716939937510582097494459230..."
[ pi.find(str(i)) for i in range(10000) ]
(PARI) A176341(n)=my(L=#Str(n)); n=Mod(n, 10^L); for(k=L1, 9e9, Pi\.1^knreturn(k+1L)) \\ Make sure to use sufficient realprecision, e.g. via \p999.  M. F. Hasler, Nov 16 2013


CROSSREFS

Cf. A000796.
Sequence in context: A062543 A086820 A174923 * A134203 A014777 A303323
Adjacent sequences: A176338 A176339 A176340 * A176342 A176343 A176344


KEYWORD

base,nonn


AUTHOR

Daniel E. Loeb, Apr 15 2010


STATUS

approved



