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 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). 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 (list; graph; refs; listen; history; text; internal format)
 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..n-1} 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..n-1} a(k), are:   n  a(n)  bin(a(n))  bin(Sum_{k=1..n-1} 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

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)