A358919 a(0) = 0, and for any n >= 0, a(n+1) is the sum of the lengths of the runs of consecutive terms a(i), ..., a(j) with 0 <= i <= j <= n such that a(i) XOR ... XOR a(j) = a(n) (where XOR denotes the bitwise XOR operator).

0, 1, 3, 1, 4, 1, 5, 5, 10, 4, 12, 18, 1, 13, 8, 22, 44, 7, 52, 1, 19, 35, 10, 43, 53, 7, 68, 1, 31, 24, 56, 73, 8, 126, 105, 35, 71, 36, 71, 60, 70, 1, 124, 180, 10, 172, 41, 182, 40, 288, 1, 232, 15, 201, 4, 271, 6, 213, 1, 233, 14, 230, 25, 216, 9, 157, 115

Offset

0,3

Comments

The sequence is unbounded (if the sequence was bounded, with greatest value m, then, by the pigeonhole principle, some value, say v, would appear infinitely many times, and the next value after the (m+1)-th occurrence of v would be > m, a contradiction).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..15722

Rémy Sigrist, C program

Rémy Sigrist, Scatterplot of the first 350000 terms

Example

The first terms, alongside the corresponding pairs (i,j), are:
  n   a(n)  (i,j)'s
  --  ----  ---------------------------------
   0     0  N/A
   1     1  (0,0)
   2     3  (0,1), (1,1)
   3     1  (2,2)
   4     4  (0,1), (1,1), (3,3)
   5     1  (4,4)
   6     5  (0,1), (1,1), (3,3), (5,5)
   7     5  (3,4), (4,5), (6,6)
   8    10  (3,4), (4,5), (4,7), (6,6), (7,7)
   9     4  (6,8), (8,8)
  10    12  (3,5), (3,7), (4,4), (5,6), (9,9)
  11    18  (0,8), (1,8), (10,10)
  12     1  (11,11)

Prog

(C) See Links section.

Crossrefs

Cf. A358799, A358918.

Sequence in context: A242746 A363258 A327642 * A354617 A324242 A216543

Adjacent sequences: A358916 A358917 A358918 * A358920 A358921 A358922

Keyword

nonn,base

Author

Rémy Sigrist, Dec 06 2022

Status

approved