

A317788


Lexicographically earliest infinite sequence of distinct positive terms such that for any n > 1, the binary representation of a(n) appears as a substring in the binary representation of Sum_{k=1..n1} a(k).


1



2, 1, 3, 6, 4, 8, 12, 9, 5, 18, 17, 10, 7, 19, 14, 16, 11, 20, 13, 24, 22, 15, 32, 36, 34, 25, 23, 37, 27, 21, 26, 64, 69, 40, 43, 29, 30, 35, 39, 44, 28, 42, 53, 129, 72, 38, 31, 81, 45, 50, 46, 47, 49, 74, 41, 54, 55, 51, 52, 57, 58, 128, 68, 70, 140, 77, 60
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OFFSET

1,1


COMMENTS

The sequence must start with a(1) = 2 in order to be infinite, and for any n > 1, a(n) <= Sum_{k=1..n1} a(k).
This sequence has similarities with A160855.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Density plot of the first 100000000 terms
Rémy Sigrist, C++ program for A317788


EXAMPLE

The first terms, alongside the binary representations of a(n) and of Sum_{k=1..n1} a(k), are:
n a(n) bin(a(n)) bin(Sum_{k=1..n1} a(k))
   
1 2 10 0
2 1 1 10
3 3 11 11
4 6 110 110
5 4 100 1100
6 8 1000 10000
7 12 1100 11000
8 9 1001 100100
9 5 101 101101
10 18 10010 110010


PROG

(C++) See Links section.


CROSSREFS

Cf. A160855.
Sequence in context: A257881 A268182 A094339 * A120576 A063707 A205840
Adjacent sequences: A317785 A317786 A317787 * A317789 A317790 A317791


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Aug 07 2018


STATUS

approved



