|
%I #31 Sep 07 2023 12:47:54
%S 1,2,3,4,6,8,11,15,20,27,36,48,64,86,115,154,206,275,367,490,654,872,
%T 1163,1551,2068,2758,3678,4904,6539,8719,11626,15502,20670,27560,
%U 36747,48996,65328,87104,116139,154852,206470,275294,367059,489412,652550
%N a(n) = ceiling(a(n-1)*4/3), with a(1) = 1.
%C 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
%H Robert Israel, <a href="/A087192/b087192.txt">Table of n, a(n) for n = 1..7994</a>
%F Partial sums of A072493. Also indices of records in A087165: A087165(a(n))=n.
%p A[1]:= 1:
%p for n from 2 to 100 do A[n]:= ceil(4/3*A[n-1]) od:
%p seq(A[i],i=1..100); # _Robert Israel_, Aug 17 2017
%t a[1] = 1; a[n_] := a[n] = Ceiling[4 a[n - 1]/3]; Table[a@ n, {n, 45}] (* _Michael De Vlieger_, Jan 06 2016 *)
%o (PARI) a(n) = if (n==1, 1, ceil(a(n-1)*4/3)) \\ _Michel Marcus_, Aug 01 2013
%o (Magma) [n eq 1 select 1 else Ceiling(Self(n-1)*4/3): n in [1..50]]; // _Vincenzo Librandi_, Aug 17 2017
%o (Python)
%o from fractions import Fraction
%o from functools import lru_cache
%o @lru_cache(maxsize=None)
%o def A087192(n): return int(Fraction(4*A087192(n-1),3).__ceil__()) if n>1 else 1 # _Chai Wah Wu_, Sep 07 2023
%Y Cf. A072493, A087165.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 24 2003
|
