A227177 - OEIS

%I #32 Nov 07 2024 15:45:45

%S 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,

%T 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,

%U 6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7

%N n occurs n^2 - n + 1 times.

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

%H Antti Karttunen, <a href="/A227177/b227177.txt">Table of n, a(n) for n = 0..9951</a>

%F a(k + (j^3-j^2+5*j)/3) = j for all j>=0, k=0..(j^2-j). - _Jinyuan Wang_, Nov 24 2018

%F 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

%t Flatten[Map[ConstantArray[#,(#-2) (#-1)+1]-1&,Range[7]]] (* _Peter J. C. Moses_, Jul 14 2013 *)

%t Flatten[Table[#,{#^2-#+1}]&/@Range[0,7]] (* _Harvey P. Dale_, Sep 25 2013 *)

%o (Scheme, with _Antti Karttunen_'s IntSeq-library): (define A227177 (LEAST-GTE-I 0 0 A006527))

%o (PARI) vec(N)=concat(vector(N, i, vector(i^2-i+1, j, i))) \\ _Jinyuan Wang_, Dec 01 2018

%o (Python)

%o from sympy import integer_nthroot

%o def A227177(n): return (m:=integer_nthroot(k:=3*n,3)[0])+(k>m*(m**2+2)) # _Chai Wah Wu_, Nov 07 2024

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

%K nonn

%O 0,3

%A _Antti Karttunen_, Jul 03 2013