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

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, 62, 66, 68, 77, 80, 78, 57, 63, 64, 66, 70, 70, 76, 82, 84, 90, 92, 81, 96, 110, 108, 118, 114, 124, 126, 130, 132, 142, 140, 144, 153, 165, 168, 174, 177, 182, 186, 171, 120

Offset: 0

Author

Reinhard Zumkeller, Dec 08 2002

Keywords

• nonn
• base

Examples

			n=10: sum of the A078822(10)=5 binary numbers: a(10) = '0'+'1'+'10'+'101'+'1010' = 0+1+2+5+10 = 18.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A078822, A078825, A007088, A144623, A144624.

Programs

Haskell

a078823 = sum . a119709_row  -- Reinhard Zumkeller, Aug 14 2013

Python

def a(n): return sum(set(((((2<>i for i in range(n.bit_length()) for l in range(n.bit_length()-i)))
print([a(n) for n in range(64)]) # Michael S. Branicky, Jul 28 2022

Formula

a(2^k-1) = 2^(k+1)-(k+2); a(2^k) = 2^(k+1)-1;

for k>0: a(2^k+1) = 2^(k+1);

a(2^k-1) = A078825(2^k-1), a(2^k) = A078825(2^k).