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A078823
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Sum of distinct binary numbers contained as substrings in binary representation of n.
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8
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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FORMULA
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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).
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EXAMPLE
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n=10: sum of the A078822(10)=5 binary numbers: a(10) = '0'+'1'+'10'+'101'+'1010' = 0+1+2+5+10 = 18.
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PROG
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(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
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CROSSREFS
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Cf. A078822, A078825, A007088, A144623, A144624.
Sequence in context: A330221 A343151 A014602 * A045615 A211220 A051201
Adjacent sequences: A078820 A078821 A078822 * A078824 A078825 A078826
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Dec 08 2002
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STATUS
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approved
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