A336190 a(n) is the least k such that A336033(k) = n.

1, 2, 5, 11, 15, 31, 39, 47, 55, 111, 119, 143, 151, 175, 183, 207, 215, 431, 439, 463, 471, 559, 567, 591, 599, 687, 695, 719, 727, 815, 823, 847, 855, 1711, 1719, 1743, 1751, 1839, 1847, 1871, 1879, 2223, 2231, 2255, 2263, 2351, 2359, 2383, 2391, 2735, 2743

Offset: 0

Author

Rémy Sigrist, Jul 11 2020

Keywords

• nonn
• base

Comments

This sequence is strictly increasing.

Examples

			The first terms, alongside A336033, are:
  n  a(n)  k   A336033(k)
  -  ----  --  ----------
  0     1   1           0
  1     2   2           1
            3           0
            4           1
  2     5   5           2
            6           0
            7           1
            8           0
            9           1
           10           2
  3    11  11           3
           12           2
           13           2
           14           3
  4    15  15           4
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, C program for A336190

Crossrefs

Cf. A002066, A336033.

Programs

C

See Links section.

PARI

{ w=0; for (n=1, #a=vector(2743), x=0; forstep (k=n-1, 1, -1, if (!x=bitxor(x, a[k]), a[n]=1+a[k]; break)); if (w==a[n], print1 (n ", "); w++)) }

Formula

Apparently, a(2^(k+1)) = a(2^k) + A002066(k-1) for k > 0.