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A064810
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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.
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4
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6, 27, 13598, 43611, 24643510, 71683711, 78714901, 268561754, 4261759184, 82638677082, 548535559133, 8773143366618
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Near-misses '04658726522' and '0769960191236' occur at positions 4658726522 and 769960191236, respectively. - Kang Seonghoon, Nov 02 2020
a(13) > 5 * 10^13. - Kang Seonghoon, Nov 02 2020
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LINKS
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Table of n, a(n) for n=1..12.
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).
L. Brandon Stone, 27 and the Number Pi.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000796, A057679, A057680.
Sequence in context: A048436 A276412 A006174 * A101454 A091911 A215896
Adjacent sequences: A064807 A064808 A064809 * A064811 A064812 A064813
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KEYWORD
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base,nonn,more
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 22 2001
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EXTENSIONS
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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
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STATUS
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approved
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