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Search: id:A053646
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| A053646 |
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Distance to nearest power of 2. |
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+0
7
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| 0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Sum {j=1..2^(k+1), a(j)} = A002450(k) = (4^k - 1)/3. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 17 2003
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LINKS
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Klaus Brockhaus, Illustration for A053646, A081252, A081253 and A081254
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FORMULA
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a(2^k+i)=i for 1<=i<=2^(k-1); a(3*2^k+i)=2^k-i for 1<=i<=2^k; sum(k=1, n, a(k))/n^2 is bounded. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002
a(n) = min(n-2^floor(log(n)/log(2)), 2*2^floor(log(n)/log(2))-n). - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 08 2003
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EXAMPLE
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a(10)=2 since 8 is closest power of 2 to 10 and |8-10|=2
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PROGRAM
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(PARI) a(n)=vecmin(vector(n, i, abs(n-2^(i-1))))
(PARI) for(n=1, 89, p=2^floor(0.1^25+log(n)/log(2)); print1(min(n-p, 2*p-n), ", "))
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CROSSREFS
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Cf. A053188, A060973, A081134, A002450, A081252, A081253, A081254.
Sequence in context: A002819 A037834 A004074 this_sequence A080776 A065358 A062329
Adjacent sequences: A053643 A053644 A053645 this_sequence A053647 A053648 A053649
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 22 2000
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