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A356150 a(n) is the sum of the positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.

%I A356150 #10 Jul 31 2022 19:54:18
%S A356150 1,3,4,10,8,12,11,25,25,18,26,28,30,33,26,56,62,61,56,56,39,63,64,67,
%T A356150 62,66,72,77,80,78,57,119,139,143,137,135,134,119,134,134,134,81,120,
%U A356150 138,139,147,142,146,147,148,132,153,140,157,165,165,168,174,181
%N A356150 a(n) is the sum of the positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.
%C A356150 Leading 0's in binary expansions are ignored.
%H A356150 Rémy Sigrist, <a href="/A356150/b356150.txt">Table of n, a(n) for n = 1..8192</a>
%H A356150 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A356150 a(n) >= A078823(n).
%F A356150 a(n) Sum_{k = 1..A356148(n)} A356149(n, k).
%e A356150 For n = 11:
%e A356150 - row 11 of A356149 is 1, 2, 3, 4, 5, 11,
%e A356150 - so a(11) = 1 + 2 + 3 + 4 + 5 + 11 = 26.
%o A356150 (PARI) a(n) = { my (b=binary(n)); vecsum(setbinop((i,j) -> my (s=fromdigits(b[i..j],2)); if (b[i], s, 2^(j-i+1)-1-s), [1..#b])) }
%o A356150 (Python)
%o A356150 def a(n):
%o A356150     N = n.bit_length()
%o A356150     c, s = ((1<<N)-1)^n, set()
%o A356150     for i in range(N):
%o A356150         for l in range(N-i):
%o A356150             mask = ((2<<l)-1) << i
%o A356150             s.add((mask&n) >> i)
%o A356150             s.add((mask&c) >> i)
%o A356150     return sum(s)
%o A356150 print([a(n) for n in range(1, 60)]) # _Michael S. Branicky_, Jul 28 2022
%Y A356150 Cf. A078823, A356148, A356149.
%K A356150 nonn,base
%O A356150 1,2
%A A356150 _Rémy Sigrist_, Jul 28 2022