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).

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

Offset: 1

Author

Rémy Sigrist, Aug 07 2018

Keywords

• nonn
• base

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.

Examples

			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
		

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

Crossrefs

Cf. A160855.