A244317 n occurs A014138(n) times.

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6

Offset: 0

Author

Antti Karttunen, Jul 18 2014

Keywords

• nonn
• easy

Comments

For n >= 1, a(n) = 1 + the least k such that A014143(k) >= n.

Useful when computing A244314.

Crossrefs

Cf. A014138, A014143, A244314, A072643, A081288, A244160.

Programs

Mathematica

Join[{0},Flatten[Table[#[[2]],#[[1]]]&/@With[{nn=6},Thread[{Join[Accumulate[ CatalanNumber[ Range[ nn]]]],Range[nn]}]]]] (* Harvey P. Dale, Sep 06 2023 *)

Scheme

(define (A244317 n) (if (zero? n) n (let loop ((k 0)) (if (>= (A014143 k) n) (+ 1 k) (loop (+ 1 k))))))

Formula

For all n >= 0, a(A014143(n)) = n+1 and a(1+A014143(n)) = n+2.