cp's OEIS Frontend

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..n-1} a(k).

%I A317788 #11 Aug 19 2018 02:47:26
%S A317788 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,
%T A317788 23,37,27,21,26,64,69,40,43,29,30,35,39,44,28,42,53,129,72,38,31,81,
%U A317788 45,50,46,47,49,74,41,54,55,51,52,57,58,128,68,70,140,77,60
%N 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..n-1} a(k).
%C A317788 The sequence must start with a(1) = 2 in order to be infinite, and for any n > 1, a(n) <= Sum_{k=1..n-1} a(k).
%C A317788 This sequence has similarities with A160855.
%H A317788 Rémy Sigrist, <a href="/A317788/b317788.txt">Table of n, a(n) for n = 1..10000</a>
%H A317788 Rémy Sigrist, <a href="/A317788/a317788.png">Density plot of the first 100000000 terms</a>
%H A317788 Rémy Sigrist, <a href="/A317788/a317788.txt">C++ program for A317788</a>
%e A317788 The first terms, alongside the binary representations of a(n) and of Sum_{k=1..n-1} a(k), are:
%e A317788   n  a(n)  bin(a(n))  bin(Sum_{k=1..n-1} a(k))
%e A317788   -- ----  ---------  ------------------------
%e A317788    1    2         10         0
%e A317788    2    1          1        10
%e A317788    3    3         11        11
%e A317788    4    6        110       110
%e A317788    5    4        100      1100
%e A317788    6    8       1000     10000
%e A317788    7   12       1100     11000
%e A317788    8    9       1001    100100
%e A317788    9    5        101    101101
%e A317788   10   18      10010    110010
%o A317788 (C++) See Links section.
%Y A317788 Cf. A160855.
%K A317788 nonn,base
%O A317788 1,1
%A A317788 _Rémy Sigrist_, Aug 07 2018