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A057679 Numbers n such that the string n is found at position n in the decimal digits of Pi. 14


%S 5,242424,271070,9292071,29133316,70421305,215817165252,649661007154

%N Numbers n such that the string n is found at position n in the decimal digits of Pi.

%C The total probability of finding a match 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

%C a(9) is greater than 10^12. - _Alan Eliasen_, Jun 17 2013

%C a(2) is not the first occurrence of 242424 in Pi (which is at position 242422) but the second. - _Hans Havermann_, Jul 26 2014

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

%t 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

%Y Cf. A000796, A057680, A064810, A109514.

%K nonn,base,more

%O 1,1

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

%E a(4)-a(6) from _Colin Rose_, Mar 15 2006

%E a(7) from _Alan Eliasen_, May 10 2013

%E a(8) from _Alan Eliasen_, Jun 06 2013

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Last modified December 11 15:43 EST 2017. Contains 295905 sequences.