cp's OEIS Frontend

A078823 Sum of distinct binary numbers contained as substrings in binary representation of n.

%I A078823 #13 Jul 31 2022 07:47:28
%S A078823 0,1,3,4,7,8,12,11,15,16,18,22,28,30,33,26,31,32,34,38,42,39,50,52,60,
%T A078823 62,66,68,77,80,78,57,63,64,66,70,70,76,82,84,90,92,81,96,110,108,118,
%U A078823 114,124,126,130,132,142,140,144,153,165,168,174,177,182,186,171,120
%N A078823 Sum of distinct binary numbers contained as substrings in binary representation of n.
%H A078823 Reinhard Zumkeller, <a href="/A078823/b078823.txt">Table of n, a(n) for n = 0..10000</a>
%F A078823 a(2^k-1) = 2^(k+1)-(k+2); a(2^k) = 2^(k+1)-1;
%F A078823 for k>0: a(2^k+1) = 2^(k+1);
%F A078823 a(2^k-1) = A078825(2^k-1), a(2^k) = A078825(2^k).
%e A078823 n=10: sum of the A078822(10)=5 binary numbers: a(10) = '0'+'1'+'10'+'101'+'1010' = 0+1+2+5+10 = 18.
%o A078823 (Haskell)
%o A078823 a078823 = sum . a119709_row  -- _Reinhard Zumkeller_, Aug 14 2013
%o A078823 (Python)
%o A078823 def a(n): return sum(set(((((2<<l)-1)<<i)&n)>>i for i in range(n.bit_length()) for l in range(n.bit_length()-i)))
%o A078823 print([a(n) for n in range(64)]) # _Michael S. Branicky_, Jul 28 2022
%Y A078823 Cf. A078822, A078825, A007088, A144623, A144624.
%K A078823 nonn,base
%O A078823 0,3
%A A078823 _Reinhard Zumkeller_, Dec 08 2002