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

Author

Kival Ngaokrajang, Mar 15 2014

Keywords

• nonn
• more
• base

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

Examples

			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
		

Crossrefs

Cf. A000796, A057680, A239316.

Programs

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 *)

Python

# Requires a text file "pib.txt" that contains the first billion digits of pi
# without a decimal point or line breaks
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
# indentation corrected by David Radcliffe, May 09 2025

Extensions

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

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