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%I #21 Sep 08 2022 08:45:16
%S 1,6,9,19,31,41,47,52,55,163,174,220,281,295,314,396,428,446,495,600,
%T 650,661,698,803,822,841,977,1090,1124,1358,1435,1501,1667,1668,1719,
%U 1828,1926,1968,1987,2007,2161,2210,2236,2261,2305,2416,2509,2555,2595
%N 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...
%C 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
%H Robert G. Wilson v, <a href="/A103186/b103186.txt">Table of n, a(n) for n = 1..9999</a>
%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">The Pi-Search Page</a>.
%H Bob Happelberg, <a href="http://www.bobspoetry.com/Bobs02Fe.pdf">Bob's Poetry Page for Feb 2005</a>
%e 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.
%t 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 *)
%o (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 */
%o (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
%Y Cf. A000796, A078197, A014777 (another version).
%K nonn,base,easy
%O 1,2
%A Suggested by Bob's Poetry Page. - _Alonso del Arte_, Mar 01 2005
%E More terms from _Graeme McRae_ and _Robert G. Wilson v_, Mar 19 2005
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