OFFSET
1,1
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
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