A227177 n occurs n^2 - n + 1 times.

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

0,3

Comments

a(n) is the least integer k such that A006527(k) >= n, which implies that each n occurs A002061(n) times.

Links

Antti Karttunen, Table of n, a(n) for n = 0..9951

Formula

a(k + (j^3-j^2+5*j)/3) = j for all j>=0, k=0..(j^2-j). - Jinyuan Wang, Nov 24 2018

a(n) = m+1 if 3n>m*(m^2+2) and a(n) = m otherwise where m=floor((3n)^(1/3)). - Chai Wah Wu, Nov 07 2024

Mathematica

Flatten[Map[ConstantArray[#, (#-2) (#-1)+1]-1&, Range[7]]] (* Peter J. C. Moses, Jul 14 2013 *)
Flatten[Table[#, {#^2-#+1}]&/@Range[0, 7]] (* Harvey P. Dale, Sep 25 2013 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library): (define A227177 (LEAST-GTE-I 0 0 A006527))
(PARI) vec(N)=concat(vector(N, i, vector(i^2-i+1, j, i))) \\ Jinyuan Wang, Dec 01 2018
(Python)
from sympy import integer_nthroot
def A227177(n): return (m:=integer_nthroot(k:=3*n, 3)[0])+(k>m*(m**2+2)) # Chai Wah Wu, Nov 07 2024

Crossrefs

Cf. A000196, A002061, A006527, A227179, A227181, A227147.

Sequence in context: A082527 A294235 A186188 * A132944 A210568 A262887

Adjacent sequences: A227174 A227175 A227176 * A227178 A227179 A227180

Keyword

nonn

Author

Antti Karttunen, Jul 03 2013

Status

approved