login
A227177
n occurs n^2 - n + 1 times.
6
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
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
KEYWORD
nonn,changed
AUTHOR
Antti Karttunen, Jul 03 2013
STATUS
approved