A368131 a(n) = floor(n * log(4/3) / log(3/2)).

0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48

Offset: 0

Author

Ruud H.G. van Tol, Jan 25 2024

Keywords

• nonn
• easy

Comments

Highest k with 3^(n+k) <= 4^n * 2^k.

Crossrefs

Cf. A054414, A117630, A325913, A369522 (slope).

Programs

Mathematica

Table[Floor[n*Log[4/3]/Log[3/2]],{n,0,68}] (* James C. McMahon, Jan 27 2024 *)

PARI

alist(N) = my(a=-1, b=1, k=0); vector(N, i, a+=2; b*=3; if(logint(b, 2) < a, a++; b*=3; k++); k); \\ note that i is n+1

Formula

a(n) = floor(n * log(3) / log(3/2)) - 2*n.

a(n) = floor(n * arctanh(1/7) / arctanh(1/5)).

a(n) = A325913(n) - n.

a(n) = A117630(n) - 2*n.

a(n) = A054414(n) - 2*n - 1.