A316993 Lexicographically earliest sequence of distinct positive terms such that a(1) = 2 and for any n > 0, the binary representation of Sum_{k=1..n} a(k) starts with the binary representation of a(n).

2, 1, 3, 5, 10, 6, 8, 4, 12, 7, 19, 11, 29, 16, 18, 21, 24, 13, 69, 39, 45, 51, 27, 14, 30, 15, 33, 17, 36, 9, 84, 96, 110, 28, 60, 31, 32, 68, 35, 75, 80, 20, 42, 43, 22, 94, 48, 50, 25, 52, 26, 55, 57, 58, 125, 64, 66, 142, 73, 37, 77, 79, 40, 41, 175, 44

Offset

1,1

Comments

This sequence is a binary variant of A316918.

This sequence is conjectured to be infinite.

This sequence is conjectured to be a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 200000 terms (where the color is function of A070939(Sum_{k=1..n} a(k)) - A070939(a(n)))

Rémy Sigrist, Scatterplot of the ordinal transform of the first 25000 terms of A070939(Sum_{k=1..n} a(k)) - A070939(a(n))

Rémy Sigrist, C++ program for A316993

Example

The first terms, alongside the binary representations of a(n) and of Sum_{k=1..n} a(k), are:
  n   a(n)  bin(a(n))  bin(Sum_{k=1..n} a(k))
  --  ----  ---------  ----------------------
   1     2         10           10
   2     1          1           11
   3     3         11          110
   4     5        101         1011
   5    10       1010        10101
   6     6        110        11011
   7     8       1000       100011
   8     4        100       100111
   9    12       1100       110011
  10     7        111       111010
  11    19      10011      1001101
  12    11       1011      1011000
  13    29      11101      1110101
  14    16      10000     10000101
  15    18      10010     10010111
  16    21      10101     10101100
  17    24      11000     11000100
  18    13       1101     11010001
  19    69    1000101    100010110
  20    39     100111    100111101

Prog

(C++) See Links section.

Crossrefs

Cf. A070939, A316918.

Sequence in context: A333177 A169912 A316994 * A092944 A049902 A096631

Adjacent sequences: A316990 A316991 A316992 * A316994 A316995 A316996

Keyword

nonn,base

Author

Rémy Sigrist, Jul 18 2018

Status

approved