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A057679
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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 3 is the first digit.
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16
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OFFSET
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1,1
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COMMENTS
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The average number of matches of length "n" digits is exactly 0.9. That is, we expect 0.9 matches with 1 digit, 0.9 matches with 2 digits, etc. Increasing the number of digits by a factor of 10 means that we expect to find 0.9 new matches. Increasing the search from 10^11 to 10^12 (which includes 10 times as much work) would thus only expect to find 0.9 new matches. - Alan Eliasen, May 01 2013 (corrected by Michael Beight, Mar 21 2020)
a(2) is not the first occurrence of 242424 in Pi (which is at position 242422) but the second. - Hans Havermann, Jul 26 2014
a(9) is greater than 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..8.
Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020).
Google, 50 trillion digits of pi (2020).
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EXAMPLE
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5 is a term because 5 is the 5th digit of Pi (3.1415...).
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MATHEMATICA
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StringsinPi[m_] := Module[{cc = 10^m + m, sol, aa}, sol = Partition[RealDigits[Pi, 10, cc] // First, m, 1]; Do[aa = FromDigits[sol[[i]]]; If[aa==i, Print[{i, aa}]], {i, Length[sol]}]; ] (* For example, StringsinPi[6] returns all 6-digit members of the sequence. - Colin Rose, Mar 15 2006 *)
dpi = RealDigits[Pi, 10, 10000010][[1]]; Select[Range[10000000], FromDigits[Take[dpi, {#, # - 1 + IntegerLength[#]}]] == # &] (* Vaclav Kotesovec, Feb 18 2020 *)
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CROSSREFS
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Cf. A000796, A057680, A064810, A109514.
Sequence in context: A243114 A038027 A237641 * A123751 A152516 A295532
Adjacent sequences: A057676 A057677 A057678 * A057680 A057681 A057682
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KEYWORD
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nonn,base,more
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AUTHOR
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Mike Keith (domnei(AT)aol.com), Oct 19 2000
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EXTENSIONS
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a(4)-a(6) from Colin Rose, Mar 15 2006
a(7) from Alan Eliasen, May 10 2013
a(8) from Alan Eliasen, Jun 06 2013
Name clarified by Kang Seonghoon, Nov 02 2020
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STATUS
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approved
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