A360265 a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that t(k) >= n (where t(m) denotes A000217(m), the m-th triangular number); a(n) = k + a(t(k) - n).

0, 1, 3, 2, 6, 4, 3, 6, 7, 5, 4, 11, 7, 8, 6, 5, 10, 12, 8, 9, 7, 6, 10, 11, 13, 9, 10, 8, 7, 14, 11, 12, 14, 10, 11, 9, 8, 16, 15, 12, 13, 15, 11, 12, 10, 9, 15, 17, 16, 13, 14, 16, 12, 13, 11, 10, 15, 16, 18, 17, 14, 15, 17, 13, 14, 12, 11, 23, 16, 17, 19

Offset

0,3

Comments

See A002024 for the corresponding k's.

See A360259 for similar sequences.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(A000217(n)) = n.

Example

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     6    3
   5     4    3
   6     3    3
   7     6    4
   8     7    4
   9     5    4
  10     4    4
  11    11    5
  12     7    5

Prog

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

Crossrefs

Cf. A000217, A002024, A360259.

Sequence in context: A195345 A057050 A182546 * A123042 A121647 A339333

Adjacent sequences: A360262 A360263 A360264 * A360266 A360267 A360268

Keyword

nonn,look

Author

Rémy Sigrist, Jan 31 2023

Status

approved