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

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

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

Dave Andersen, 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

a(n) = 0 if n is in A011545, otherwise a(n) = A014777(n). - Pontus von Brömssen, Aug 31 2024

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=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

Crossrefs

Cf. A000796, A011545, A014777, A032445, A232013.

Sequence in context: A174923 A369651 A351809 * A134203 A014777 A303323

Adjacent sequences: A176338 A176339 A176340 * A176342 A176343 A176344

Keyword

base,nonn

Author

Daniel E. Loeb, Apr 15 2010

Status

approved