A239317 Index of the first occurrence of a string of exactly n even numbers in the decimal expansion of Pi.

3, 7, 53, 117, 33, 19, 965, 372, 1834, 70, 5876, 8878, 9288, 1279, 173580, 248625, 652113, 678288, 2199379, 1656691, 3455554, 30021792, 18707922, 26568757, 189709607, 36454145, 255896738, 388817627

Offset

1,1

Comments

a(29) > 10^9

The string of even digits of length n must be preceded and followed by an odd digit. - Harvey P. Dale, Jan 27 2022

Links

Table of n, a(n) for n=1..28.

Example

Digit:         1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...
Pi:            3 1 4 1 5 9 2 6 5  3  5  8  9  7  9 ...
Even string:   ...[1]......[2].........[1]............
                   .        .
                   .        .
                  a(1)     a(2)
                  = 3      = 7

Mathematica

Module[{nn=389*10^6, dep}, dep=If[EvenQ[#], 1, 0]&/@RealDigits[Pi, 10, nn][[1]]; Table[SequencePosition[dep, Join[{0}, PadLeft[{0}, n, 1]], 1][[1]], {n, 2, 29}][[All, 1]]]+1 (* Harvey P. Dale, Jan 27 2022 *)

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 == 0:#digit is odd
....................now += 1
................else:
....................now = 0
................if now == a and c%2 == 1:
....................print(a, place-a+2)
....................found = True
....................break
................place += 1
........if not found:
............print("Not found in first billion digits.")
# David Consiglio, Jr., Sep 22 2014

Crossrefs

Cf. A000796, A057680, A239316.

Sequence in context: A207138 A041277 A248239 * A058023 A285065 A095124

Adjacent sequences: A239314 A239315 A239316 * A239318 A239319 A239320

Keyword

nonn,more,base

Author

Kival Ngaokrajang, Mar 15 2014

Extensions

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

Corrected and definition clarified by Harvey P. Dale, Jan 27 2022

Status

approved