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

%I A084187 #22 Feb 15 2024 19:00:31
%S A084187 2,15,63,58,9,1003,524,454,1303,5335,22472,8882,37469,32279,220311,
%T A084187 92988,698343,24002,574131,3333660,5940559,4079882,8356569,115885798,
%U A084187 76570753,202460870,1034477781,457034356,1005210009,3753736439,2204906858,50747186116,32242071604,159423417084,114244391078,74632918239
%N A084187 First occurrence of exactly n 0's in the binary expansion of sqrt(2).
%e A084187 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.
%t A084187 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 *)
%o A084187 (Python)
%o A084187 from math import isqrt
%o A084187 from itertools import count
%o A084187 def A084187(n):
%o A084187     a, b = 2, (1<<n+2)-1
%o A084187     c = (b+1>>1)|1
%o A084187     for k in count(1-n):
%o A084187         if isqrt(a)&b==c:
%o A084187             return k
%o A084187         a<<=2 # _Chai Wah Wu_, Jan 25 2024
%o A084187 (C) See Links section of A084186.
%Y A084187 Cf. A084185, A084186.
%Y A084187 Cf. A233836.
%K A084187 nonn,hard
%O A084187 1,1
%A A084187 _Ralf Stephan_, May 18 2003
%E A084187 More terms from _Ryan Propper_, May 09 2006
%E A084187 a(26)-a(29) from _Chai Wah Wu_, Jan 25 2024
%E A084187 a(30)-a(36) from _Nick Hobson_, Feb 15 2024