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.
6, 27, 13598, 43611, 24643510, 71683711, 78714901, 268561754, 4261759184, 82638677082, 548535559133, 8773143366618
Offset: 1
Examples
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.
Links
- Dave Andersen, The Pi-Search Page.
- Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020).
- Brady Haran and Katie Steckles, 27 the Favourite Number, Numberphile video (2012).
- Timothy Mullican, 50 trillion digits of pi (2020). Last backup of the googleAPIs.com page on web.archive.org, as of June 2022.
- L. Brandon Stone, 27 and the Number Pi, personal web site. Last backup on web.archive.org as of Oct. 2004.
Programs
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Mathematica
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 *) -
Python
# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then with open('pi-billion.txt', 'r') as f: digits_of_pi = f.readline()[2:] # from sympy import S, isprime # digits_of_pi = str(S.Pi.n(3*10**5))[2:] # alternate to loading data def afind(): global digits_of_pi for k in range(len(digits_of_pi)): s = str(k) if digits_of_pi[k:k+len(s)] == s: print(k, end=", ") afind() # Michael S. Branicky, Jun 27 2021
Extensions
a(6)-a(10) from Alan Eliasen, May 11 2013
a(11) from Alan Eliasen, May 28 2013
a(12) added and name clarified by Kang Seonghoon, Nov 02 2020
Error in a(11) reported by Sergey Prokudin, edited by Robert Price, Mar 14 2022
Comments