

A113474


a(n) = a(floor(n/2)) + floor(n/2) with a(1) = 1.


2



1, 2, 2, 4, 4, 5, 5, 8, 8, 9, 9, 11, 11, 12, 12, 16, 16, 17, 17, 19, 19, 20, 20, 23, 23, 24, 24, 26, 26, 27, 27, 32, 32, 33, 33, 35, 35, 36, 36, 39, 39, 40, 40, 42, 42, 43, 43, 47, 47, 48, 48, 50, 50, 51, 51, 54, 54, 55, 55, 57, 57, 58, 58, 64, 64, 65, 65, 67, 67, 68, 68, 71, 71
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OFFSET

1,2


COMMENTS

a(2^n) = 2^n, in other cases a(n) < n; except for the first one all entries are repeated twice; apparently no simple formula for a(n).
Taking every other term seems to give A101925.  Dominick Cancilla, Aug 03 2010


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2500
Tanya Khovanova, There are no coincidences, arXiv:1410.2193 [math.CO], 2014.


FORMULA

From Paul Barry, Aug 27 2006: (Start)
a(n) = ( Sum_{k=0..n} floor(n/2^k) )  n + 1.
a(n) = 2 + Sum_{k=0..n} ( floor(n/2^k)1 ).
a(n) = A005187(n)  n + 1. (End)
a(n) = n + O(log n).  Charles R Greathouse IV, Mar 12 2017


MATHEMATICA

a[1]=1; a[n_]:=a[n]=a[Floor[n/2]]+Floor[n/2]; Table[a[n], {n, 100}]


PROG

(PARI) for(n=1, 75, print1(1  n + sum(k=0, n, n\2^k), ", ")) \\ G. C. Greubel, Mar 11 2017
(PARI) a(n)=sum(k=1, logint(n, 2), n>>k)+1 \\ Charles R Greathouse IV, Mar 12 2017


CROSSREFS

Sequence in context: A035644 A288773 A288774 * A089413 A159267 A127311
Adjacent sequences: A113471 A113472 A113473 * A113475 A113476 A113477


KEYWORD

nonn,easy


AUTHOR

Zak Seidov, Jan 08 2006


STATUS

approved



