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A351964 The 2-adic valuation of A109812(n); The exponent of the highest power of 2 dividing A109812(n).

%I A351964 #13 Jul 16 2022 11:32:08
%S A351964 0,1,2,0,3,0,1,4,1,0,1,2,0,1,5,0,3,0,2,0,2,0,3,0,1,0,4,0,6,1,0,1,0,1,
%T A351964 0,1,0,3,0,5,0,2,0,2,0,2,4,0,3,7,0,1,0,1,0,1,0,1,2,1,0,1,0,2,1,0,1,3,
%U A351964 0,3,0,2,0,2,6,0,5,0,4,0,2,0,1,0,1,0,1,0,1,0,1,0,1,0,1,2,0,4,0,1,2,0,8,0,4
%N A351964 The 2-adic valuation of A109812(n); The exponent of the highest power of 2 dividing A109812(n).
%H A351964 Antti Karttunen, <a href="/A351964/b351964.txt">Table of n, a(n) for n = 1..100000</a>
%H A351964 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A351964 a(n) = A007814(A109812(n)).
%o A351964 (PARI)
%o A351964 v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
%o A351964 up_to = #v109812;
%o A351964 A109812(n) = v109812[n];
%o A351964 A007814(n) = valuation(n,2);
%o A351964 A351964(n) = A007814(A109812(n));
%o A351964 (Python)
%o A351964 from itertools import count, islice
%o A351964 def A351964_gen(): # generator of terms
%o A351964     yield 0
%o A351964     l1, s, b = 1, 2, set()
%o A351964     while True:
%o A351964         for i in count(s):
%o A351964             if not (i in b or i & l1):
%o A351964                 yield (~i&i-1).bit_length()
%o A351964                 l1 = i
%o A351964                 b.add(i)
%o A351964                 while s in b:
%o A351964                     b.remove(s)
%o A351964                     s += 1
%o A351964                 break
%o A351964 A351964_list = list(islice(A351964_gen(),30)) # _Chai Wah Wu_, Jul 16 2022
%Y A351964 Cf. A007814, A109812, A351578, A351965.
%K A351964 nonn,base
%O A351964 1,3
%A A351964 _Antti Karttunen_, Apr 07 2022