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

0,3

Links

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

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).

Example

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

Prog

(Haskell)
a078823 = sum . a119709_row  -- Reinhard Zumkeller, Aug 14 2013
(Python)
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)))
print([a(n) for n in range(64)]) # Michael S. Branicky, Jul 28 2022

Crossrefs

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

Sequence in context: A330221 A343151 A014602 * A045615 A211220 A051201

Adjacent sequences: A078820 A078821 A078822 * A078824 A078825 A078826

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 08 2002

Status

approved