A360260 a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that T(3) + ... + T(2+k) >= n (where T(m) denotes A000073(m), the m-th tribonacci number); a(n) = k + a(T(3) + ... + T(2+k) - n).

0, 1, 3, 2, 5, 6, 4, 3, 8, 10, 9, 6, 7, 5, 4, 12, 11, 14, 15, 13, 8, 9, 11, 10, 7, 8, 6, 5, 16, 17, 15, 14, 19, 21, 20, 17, 18, 10, 11, 13, 12, 15, 16, 14, 9, 10, 12, 11, 8, 9, 7, 6, 21, 23, 22, 19, 20, 18, 17, 25, 24, 27, 28, 26, 21, 22, 24, 23, 12, 13, 15

Offset: 0

Author

Rémy Sigrist, Jan 31 2023

Keywords

• nonn
• look

Comments

See A356895 for the corresponding k's.

See A360259 for the Fibonacci variant.

Examples

			The first terms, alongside the corresponding k's, are:
  n   a(n)  k
  --  ----  ---
   0     0  N/A
   1     1    1
   2     3    2
   3     2    2
   4     5    3
   5     6    3
   6     4    3
   7     3    3
   8     8    4
   9    10    4
  10     9    4
  11     6    4
  12     7    4
  13     5    4
  14     4    4
  15    12    5
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10609

Crossrefs

Cf. A000073, A027084, A356895, A360259.

Programs

PARI

tribonacci(n) = ([0,1,0; 0,0,1; 1,1,1]^n)[2,1]
{ t = k = 0; print1 (0); for (n = 1, #a = vector(70), if (n > t, t += tribonacci(2+k++);); print1 (", "a[n] = k+if (t==n, 0, a[t-n]));); }

Formula

a(A027084(n)) = n - 1.