A377722 - OEIS

%I #11 Nov 06 2024 04:31:36

%S 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N n appears n^4 times.

%H Paolo Xausa, <a href="/A377722/b377722.txt">Table of n, a(n) for n = 1..15333</a>

%F a(n) = m+1 if n>m(m+1)(2m+1)(3m^2+3m-1)/30 and a(n) = m otherwise where m = floor((5n)^(1/5)).

%F For a sequence a_k(n) where n appears n^(k-1) times, a_k(n) = m+1 if n > Sum_{i=1..m} i^(k-1) and a_k(n) = m otherwise where m = floor((kn)^(1/k)).

%t A377722[n_] := # + Boole[n > #*(# + 1)*(2*# + 1)*(3*#^2 + 3*# - 1)/30] & [Floor[(5*n)^(1/5)]];

%t Array[A377722, 354] (* or *)

%t Flatten[Table[k, {k, 4}, {k^4}]] (* _Paolo Xausa_, Nov 05 2024 *)

%o (Python)

%o from sympy import integer_nthroot

%o def A377722(n): return (m:=integer_nthroot(5*n,5)[0])+(30*n>m*(m+1)*((m<<1)+1)*(3*m*(m+1)-1))

%Y Cf. A002024, A074279, A108582.

%K nonn

%O 1,2

%A _Chai Wah Wu_, Nov 04 2024