

A160855


a(n) = the smallest positive integer not occurring earlier in the sequence such that sum{k=1 to n} a(k) written in binary contains binary n as a substring.


4



1, 3, 2, 6, 8, 4, 5, 11, 10, 24, 12, 13, 7, 9, 28, 17, 36, 14, 20, 46, 22, 44, 25, 18, 15, 16, 19, 21, 23, 26, 38, 33, 68, 30, 37, 29, 65, 39, 27, 57, 50, 88, 45, 85, 47, 83, 48, 34, 49, 51, 79, 53, 56, 32, 31, 35, 40, 41, 42, 63, 58, 72, 64, 66, 69, 61, 129, 93, 106, 60, 86
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OFFSET

1,2


COMMENTS

Is this a permutation of the positive integers?
The smallest number not in {a(n)  n<=8000000} is 5083527. It appears that the quotient (a(1)+...+a(n))/n^2 meanders around between 1/2 (=perfect permutation) and 2/3: at n=8000000 the value is approximately 0.5866 (does it converge? 1/2? Golden ratio?).
The scatterplot of the first 100000 terms (see "graph") has some remarkable features which have not yet been explained  Leroy Quet, Jul 05 2009
a(A236341(n)) = n.  Reinhard Zumkeller, Jul 12 2015


LINKS

H. v. Eitzen, Table of n, a(n) for n=1..100000


PROG

(Haskell)
import Data.List (delete)
a160855 n = a160855_list !! (n  1)
a160855_list = 1 : f 2 1 [2..] where
f x sum zs = g zs where
g (y:ys) = if binSub x (sum + y)
then y : f (x + 1) (sum + y) (delete y zs) else g ys
binSub u = sub where
sub w = mod w m == u  w > u && sub (div w 2)
m = a062383 u
 Reinhard Zumkeller, Jul 12 2015


CROSSREFS

Cf. A160856.
Cf. A062383, A236341 (putative inverse).
Sequence in context: A210236 A193998 A209171 * A120232 A019444 A195412
Adjacent sequences: A160852 A160853 A160854 * A160856 A160857 A160858


KEYWORD

nonn,base,look


AUTHOR

Leroy Quet, May 28 2009


EXTENSIONS

Extended by Ray Chandler, Jun 15 2009


STATUS

approved



