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A064810 Self-locating strings within Pi: numbers n such that the string n is at position n in the decimal digits of Pi, where 1 is the 0th digit. 5

%I #60 Apr 25 2022 08:03:29

%S 6,27,13598,43611,24643510,71683711,78714901,268561754,4261759184,

%T 82638677082,548535559133,8773143366618

%N Self-locating strings within Pi: numbers n such that the string n is at position n in the decimal digits of Pi, where 1 is the 0th digit.

%C Near-misses '04658726522' and '0769960191236' occur at positions 4658726522 and 769960191236, respectively. - _Kang Seonghoon_, Nov 02 2020

%C a(13) > 5 * 10^13. - _Kang Seonghoon_, Nov 02 2020

%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">The Pi-Search Page</a>.

%H Tom Crawford and Brady Haran, <a href="https://www.youtube.com/watch?v=W20aT14t8Pw">Strings and Loops within Pi</a>, Numberphile video (2020).

%H Brady Haran and Katie Steckles, <a href="http://www.youtube.com/watch?v=euAHY9hqRN4">27 the Favourite Number</a>, Numberphile video (2012).

%H Timothy Mullican, <a href="https://storage.googleapis.com/pi50t/index.html">50 trillion digits of pi</a> (2020).

%H L. Brandon Stone, <a href="http://www.lbstone.com/27/science/pi.html">27 and the Number Pi</a>.

%e 6 is the first term because Pi is 3.1415926... and the digit 6 is in position 6 after the decimal point when the first 1 after the decimal point is considered to be at position 0.

%t Do[If[RealDigits[Pi,10,a=i+IntegerLength@i-1,-2][[1,i;;a]]==IntegerDigits@i,Print@i],{i,50000}] (* _Giorgos Kalogeropoulos_, Feb 21 2020 *)

%o (Python)

%o # download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then

%o with open('pi-billion.txt', 'r') as f: digits_of_pi = f.readline()[2:]

%o # from sympy import S, isprime

%o # digits_of_pi = str(S.Pi.n(3*10**5))[2:] # alternate to loading data

%o def afind():

%o global digits_of_pi

%o for k in range(len(digits_of_pi)):

%o s = str(k)

%o if digits_of_pi[k:k+len(s)] == s: print(k, end=", ")

%o afind() # _Michael S. Branicky_, Jun 27 2021

%Y Cf. A000796, A057679, A057680.

%K base,nonn,more

%O 1,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 22 2001

%E a(6)-a(10) from _Alan Eliasen_, May 11 2013

%E a(11) from _Alan Eliasen_, May 28 2013

%E a(12) added and name clarified by _Kang Seonghoon_, Nov 02 2020

%E Error in a(11) reported by Sergey Prokudin, edited by _Robert Price_, Mar 14 2022

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Last modified November 28 07:52 EST 2023. Contains 367394 sequences. (Running on oeis4.)