A087192 a(n) = ceiling(a(n-1)*4/3), with a(1) = 1.

1, 2, 3, 4, 6, 8, 11, 15, 20, 27, 36, 48, 64, 86, 115, 154, 206, 275, 367, 490, 654, 872, 1163, 1551, 2068, 2758, 3678, 4904, 6539, 8719, 11626, 15502, 20670, 27560, 36747, 48996, 65328, 87104, 116139, 154852, 206470, 275294, 367059, 489412, 652550

Offset: 1

Author

Paul D. Hanna, Aug 24 2003

Keywords

• nonn

Comments

If you repeatedly base 64 encode a string, starting with a single character, the length of the string at step n is 4*a(n). - Christian Perfect, Jan 06 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..7994

Crossrefs

Cf. A072493, A087165, A155167.

Programs

Magma

[n eq 1 select 1 else Ceiling(Self(n-1)*4/3): n in [1..50]]; // Vincenzo Librandi, Aug 17 2017

Maple

A[1]:= 1:
for n from 2 to 100 do A[n]:= ceil(4/3*A[n-1]) od:
seq(A[i],i=1..100); # Robert Israel, Aug 17 2017

Mathematica

a[1] = 1; a[n_] := a[n] = Ceiling[4 a[n - 1]/3]; Table[a@ n, {n, 45}] (* Michael De Vlieger, Jan 06 2016 *)

PARI

a(n) = if (n==1, 1, ceil(a(n-1)*4/3)) \\ Michel Marcus, Aug 01 2013

Python

from fractions import Fraction
from functools import lru_cache
@lru_cache(maxsize=None)
def A087192(n): return int(Fraction(4*A087192(n-1),3)._ceil_()) if n>1 else 1 # Chai Wah Wu, Sep 07 2023

Formula

Partial sums of A072493. Also indices of records in A087165: A087165(a(n))=n.