A084187 First occurrence of exactly n 0's in the binary expansion of sqrt(2).

2, 15, 63, 58, 9, 1003, 524, 454, 1303, 5335, 22472, 8882, 37469, 32279, 220311, 92988, 698343, 24002, 574131, 3333660, 5940559, 4079882, 8356569, 115885798, 76570753, 202460870, 1034477781, 457034356, 1005210009, 3753736439, 2204906858, 50747186116, 32242071604, 159423417084, 114244391078, 74632918239

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

The binary expansion of sqrt(2) is 1.0110101000001..(A004539) and at position 9, there are five 0's, framed by 1's, so a(5)=9.

Mathematica

With[{d=RealDigits[Sqrt[2], 2, 116*10^6][[1]]}, Flatten[Table[SequencePosition[d, Join[ {1}, PadRight[{}, n, 0], {1}], 1][[All, 1]], {n, 25}]]]+1 (* Harvey P. Dale, Dec 12 2022 *)

Prog

(Python)
from math import isqrt
from itertools import count
def A084187(n):
    a, b = 2, (1<<n+2)-1
    c = (b+1>>1)|1
    for k in count(1-n):
        if isqrt(a)&b==c:
            return k
        a<<=2 # Chai Wah Wu, Jan 25 2024
(C) See Links section of A084186.

Crossrefs

Cf. A084185, A084186.

Cf. A233836.

Sequence in context: A296661 A000181 A047146 * A267596 A119904 A271828

Adjacent sequences: A084184 A084185 A084186 * A084188 A084189 A084190

Keyword

nonn,hard

Author

Ralf Stephan, May 18 2003

Extensions

More terms from Ryan Propper, May 09 2006

a(26)-a(29) from Chai Wah Wu, Jan 25 2024

a(30)-a(36) from Nick Hobson, Feb 15 2024

Status

approved