A084186 First occurrence of exactly n 1's in the binary expansion of sqrt(2).

1, 3, 40, 17, 74, 265, 31, 336, 11937, 1403, 8894, 3524, 33223, 126903, 3067, 109312, 390536, 553171, 280266, 962560, 1747112, 1740081, 30793169, 13109551, 118101037, 1077718187, 44908294, 1528865059, 1647265647, 3913429742, 10501492774, 4702573600, 81557258556, 107498528405

Offset: 1

Author

Ralf Stephan, May 18 2003

Keywords

• base
• nonn
• hard

Examples

			The binary expansion of sqrt(2) is 1.0110101000001..(A004539) and at position 17, there are four 1's, framed by 0's, so a(4)=17.
		

Links

• Nick Hobson, C program

Crossrefs

Cf. A084185, A084187.

Cf. A233836.

Programs

C

See Links section.

Python

from itertools import count
from math import isqrt
def A084186(n):
    a, b = 2, (1<>1)^1
    for k in count(1-n):
        if isqrt(a)&b==c:
            return k
        a<<=2 # Chai Wah Wu, Jan 24 2024

Extensions

a(21)-a(29) from Chai Wah Wu, Jan 25 2024

a(30)-a(34) from Nick Hobson, Feb 15 2024