

A103186


a(n) is the position of the start of the first occurrence of n > a(n1) after the decimal point in Pi = 3.14159265358979323846264338327950288...


4



1, 6, 9, 19, 31, 41, 47, 52, 55, 163, 174, 220, 281, 295, 314, 396, 428, 446, 495, 600, 650, 661, 698, 803, 822, 841, 977, 1090, 1124, 1358, 1435, 1501, 1667, 1668, 1719, 1828, 1926, 1968, 1987, 2007, 2161, 2210, 2236, 2261, 2305, 2416, 2509, 2555, 2595
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OFFSET

1,2


COMMENTS

The digits at position 1667 are "334", so according to the strict definition of this sequence, a(33) is 1667 and a(34) is 1668. However, this would not enable a person to mark in boldface the counting numbers within the digits of pi, which was the inspiration for this sequence. Surprisingly, if overlapping is not allowed, this changes only one element of the sequence. a(34) becomes 1700 and a(35) remains 1719. No other overlapping occurs within the first 100,000 decimal digits of Pi.  Graeme McRae, Mar 20 2005


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..9999 . [From Robert G. Wilson v, May 20 2010]
Dave Andersen, The PiSearch Page.
Bob Happelberg, Bob's Poetry Page for Feb 2005


EXAMPLE

Moving always to the right in the decimal expansion of Pi, the string "1" is found at position 1 counting from the first digit after the decimal point, the string "2" is found at position 6, the string "3" at position 6, the string "4" at position 19, etc.


MATHEMATICA

p = ToString[ FromDigits[ RealDigits[ N[Pi  3, 2600]][[1]]]]; lst = {0}; Do[a = StringPosition[p, ToString[n], 1][[1, 1]]; AppendTo[lst, a + lst[[ 1]]]; p = StringDrop[p, a], {n, 49}]; Rest[lst] (* Robert G. Wilson v, Mar 19 2005 *)


PROG

(MAGMA) k := 3000; R := RealField(k); S := IntegerToString(Round(10^k*(3 + Pi(R)))); Q := []; d := 0; for n in [1..49] do p:= Position(S, IntegerToString(n)); d+:=p; Append(~Q, d); S := Substring(S, p+1, #Sp); end for; Q; /* Klaus Brockhaus, Feb 15 2007 */


CROSSREFS

Cf. A000796, A078197, A014777 (another version).
Sequence in context: A265099 A023041 A118277 * A011988 A161782 A154783
Adjacent sequences: A103183 A103184 A103185 * A103187 A103188 A103189


KEYWORD

nonn,base,easy


AUTHOR

Suggested by Bob's Poetry Page.  Alonso del Arte, Mar 01 2005


EXTENSIONS

More terms from Graeme McRae and Robert G. Wilson v, Mar 19 2005


STATUS

approved



