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

Author

Antti Karttunen, Jul 03 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

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

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