cp's OEIS Frontend

A356385 First differences of A353654 which is numbers with the same number of trailing 0 bits as other 0 bits.

%I A356385 #53 Nov 07 2024 11:12:06
%S A356385 2,4,3,5,7,4,5,5,10,8,4,5,13,8,10,6,10,8,4,5,9,20,16,8,10,14,8,10,6,
%T A356385 10,8,4,5,25,16,20,12,20,16,8,10,10,20,16,8,10,14,8,10,6,10,8,4,5,17,
%U A356385 40,32,16,20,28,16,20,12,20,16,8,10,26,16,20,12,20,16
%N A356385 First differences of A353654 which is numbers with the same number of trailing 0 bits as other 0 bits.
%F A356385 a(n) = A353654(n+1) - A353654(n) for n > 0.
%F A356385 a(A000045(n)-1) = 5 for n > 4.
%t A356385 Differences @ Join[{1}, Select[Range[2, 1000], IntegerExponent[#, 2] == Floor[Log2[# - 1]] - DigitCount[# - 1, 2, 1] &]] (* _Amiram Eldar_, Sep 21 2022 *)
%o A356385 (PARI) isok(k) = if (k==1, 1, (logint(k-1, 2)-hammingweight(k-1) == valuation(k, 2))); \\ A353654
%o A356385 lista(nn) = my(v=select(isok, [1..nn])); vector(#v-1, k, v[k+1] - v[k]); \\ _Michel Marcus_, Sep 21 2022
%o A356385 (Python 3.10+)
%o A356385 from itertools import pairwise, count, islice
%o A356385 def A356385_gen(): # generator of terms
%o A356385     return map(lambda x:x[1]-x[0],pairwise(filter(lambda n:(~n & n-1).bit_length()<<1 == n.bit_length()-n.bit_count(),count(1))))
%o A356385 A356385_list = list(islice(A356385_gen(),30)) # _Chai Wah Wu_, Oct 14 2022
%Y A356385 Cf. A000045, A353654.
%K A356385 nonn,base
%O A356385 1,1
%A A356385 _Mikhail Kurkov_, Aug 05 2022