A239316 Index of the first occurrence of a string of exactly n consecutive odd digits in the decimal expansion of Pi.

18, 1, 4, 13, 282, 342, 783, 43, 4424, 412, 940, 8337, 44968, 61667, 33821, 106904, 336404, 421527, 31488, 1850725, 5854551, 8996526, 11709660, 2493200, 105887707, 86401248, 701257139, 546257302, 92438127

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

Digit:       1 2 3 4 5 6 7 8 9 10 11 12 ...18 ...
Pi:          3 1 4 1 5 9 2 6 5  3  5  8 ....3 ...
Odd string:  [2]...[ 3 ].....[  3  ].......[1]...
             .       .                      .
             .       .                      .
            a(2)    a(3)                   a(1)
            = 1     = 4                    = 18

Mathematica

a239316[n_, checkDigits_: 100000] :=
Block[{foundPos,
   piDigitBooleans = {#1[[1]],
       Length[#]} & /@ (OddQ /@
        RealDigits[N[Pi, checkDigits]][[1, 1 ;; All]] // Split)},
  foundPos = FirstPosition[piDigitBooleans, {True, n}][[1]];
  If[! NumericQ[foundPos],
   Return["Not found within " <> ToString[checkDigits] <> " digits"]];
   Total[piDigitBooleans[[1 ;; foundPos]][[All, 2]]] - n + 1]
a239316[#] & /@ Range[1, 15] (* Julien Kluge, Jan 31 2016 *)

Prog

(Python)
with open("pib.txt") as f:
....digits = f.read(1000000000)
....for a in range(1, 30):
........found = False
........place = 0
........now = 0
........while place < 999999999:
............b = int(digits[place])
............c = int(digits[place+1])
............if b % 2 == 1:#digit is odd
................now += 1
............else:
................now = 0
............if now == a and c%2 == 0:
................print(a, place-a+2)
................found = True
................break
............place += 1
........if not found:
............print("Not found in first billion digits.")
# pib.txt is the first billion digits of pi, readily available online
# David Consiglio, Jr., Sep 22 2014

Crossrefs

Cf. A000796, A057680, A239317.

Sequence in context: A040334 A040333 A040335 * A040336 A040337 A152209

Adjacent sequences: A239313 A239314 A239315 * A239317 A239318 A239319

Keyword

nonn,base

Author

Kival Ngaokrajang, Mar 15 2014

Extensions

More terms from David Consiglio, Jr., Sep 22 2014

Status

approved