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A057679 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. 16
5, 242424, 271070, 9292071, 29133316, 70421305, 215817165252, 649661007154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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).

EXAMPLE

5 is a term because 5 is the 5th digit of Pi (3.1415...).

MATHEMATICA

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 *)

CROSSREFS

Cf. A000796, A057680, A064810, A109514.

Sequence in context: A243114 A038027 A237641 * A123751 A152516 A295532

Adjacent sequences:  A057676 A057677 A057678 * A057680 A057681 A057682

KEYWORD

nonn,base,more

AUTHOR

Mike Keith (domnei(AT)aol.com), Oct 19 2000

EXTENSIONS

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

STATUS

approved

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Last modified January 23 19:03 EST 2021. Contains 340386 sequences. (Running on oeis4.)