A103186 a(n) is the position of the start of the first occurrence of n > a(n-1) after the decimal point in Pi = 3.14159265358979323846264338327950288...

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

Offset: 1

Author

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

Keywords

• nonn
• base
• easy

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 bold-face 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

Examples

			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.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..9999
• Dave Andersen, The Pi-Search Page.
• Bob Happelberg, Bob's Poetry Page for Feb 2005

Crossrefs

Cf. A000796, A078197, A014777 (another version).

Programs

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, #S-p); end for; Q; /* Klaus Brockhaus, Feb 15 2007 */

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 *)

PARI

lista(nn, t=10^5) = {default(realprecision, t); my(d, k, v=digits(floor(Pi*10^t))); for(n=1, nn, d=digits(n); until(v[k+1..k+#d]==d, k++); print1(k, ", ")); } \\ Jinyuan Wang, Feb 18 2021

Extensions

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