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

%I A084186 #27 Feb 15 2024 17:28:10
%S A084186 1,3,40,17,74,265,31,336,11937,1403,8894,3524,33223,126903,3067,
%T A084186 109312,390536,553171,280266,962560,1747112,1740081,30793169,13109551,
%U A084186 118101037,1077718187,44908294,1528865059,1647265647,3913429742,10501492774,4702573600,81557258556,107498528405
%N A084186 First occurrence of exactly n 1's in the binary expansion of sqrt(2).
%H A084186 Nick Hobson, <a href="/A084186/a084186.c.txt">C program</a>
%e A084186 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.
%o A084186 (Python)
%o A084186 from itertools import count
%o A084186 from math import isqrt
%o A084186 def A084186(n):
%o A084186     a, b = 2, (1<<n+2)-1
%o A084186     c = (b>>1)^1
%o A084186     for k in count(1-n):
%o A084186         if isqrt(a)&b==c:
%o A084186             return k
%o A084186         a<<=2 # _Chai Wah Wu_, Jan 24 2024
%o A084186 (C) See Links section.
%Y A084186 Cf. A084185, A084187.
%Y A084186 Cf. A233836.
%K A084186 base,nonn,hard
%O A084186 1,2
%A A084186 _Ralf Stephan_, May 18 2003
%E A084186 a(21)-a(29) from _Chai Wah Wu_, Jan 25 2024
%E A084186 a(30)-a(34) from _Nick Hobson_, Feb 15 2024