

A053646


Distance to nearest power of 2.


14



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
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OFFSET

1,6


COMMENTS

Sum_{j=1..2^(k+1)} a(j) = A002450(k) = (4^k  1)/3.  Klaus Brockhaus, Mar 17 2003


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Klaus Brockhaus, Illustration for A053646, A081252, A081253 and A081254
HsienKuei Hwang, S. Janson, T.H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint 2016.
HsienKuei Hwang, S. Janson, T.H. Tsai, Exact and Asymptotic Solutions of a DivideandConquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.
Index entries for sequences related to distance to nearest element of some set


FORMULA

a(2^k+i) = i for 1 <= i <= 2^(k1); a(3*2^k+i) = 2^ki for 1 <= i <= 2^k; (Sum_{k=1..n} a(k))/n^2 is bounded.  Benoit Cloitre, Aug 17 2002
a(n) = min(n2^floor(log(n)/log(2)), 2*2^floor(log(n)/log(2))n).  Klaus Brockhaus, Mar 08 2003


EXAMPLE

a(10)=2 since 8 is closest power of 2 to 10 and 810 = 2.


MATHEMATICA

np2[n_]:=Module[{min=Floor[Log[2, n]], max}, max=min+1; If[2^maxn<n2^min, 2^maxn, n2^min]]; np2/@Range[90] (* Harvey P. Dale, Feb 21 2012 *)


PROG

(PARI) a(n)=vecmin(vector(n, i, abs(n2^(i1))))
(PARI) for(n=1, 89, p=2^floor(0.1^25+log(n)/log(2)); print1(min(np, 2*pn), ", "))
(PARI) a(n) = my (p=#binary(n)); return (min(n2^(p1), 2^pn)) \\ Rémy Sigrist, Mar 24 2018


CROSSREFS

Cf. A053188, A060973, A081134, A002450, A081252, A081253, A081254.
Sequence in context: A179765 A004074 A245615 * A080776 A297158 A065358
Adjacent sequences: A053643 A053644 A053645 * A053647 A053648 A053649


KEYWORD

easy,nonn


AUTHOR

Henry Bottomley, Mar 22 2000


STATUS

approved



