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

1,2

Links

Table of n, a(n) for n=1..34.

Nick Hobson, C program

Example

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.

Prog

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

Crossrefs

Cf. A084185, A084187.

Cf. A233836.

Sequence in context: A319955 A317484 A196159 * A037104 A100306 A101014

Adjacent sequences: A084183 A084184 A084185 * A084187 A084188 A084189

Keyword

base,nonn,hard

Author

Ralf Stephan, May 18 2003

Extensions

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

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

Status

approved