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A017981 Powers of cube root of 2 rounded up.

%I A017981 #28 Jul 08 2025 06:20:36
%S A017981 1,2,2,2,3,4,4,6,7,8,11,13,16,21,26,32,41,51,64,81,102,128,162,204,
%T A017981 256,323,407,512,646,813,1024,1291,1626,2048,2581,3251,4096,5161,6502,
%U A017981 8192,10322,13004,16384,20643,26008,32768,41286,52016,65536,82571,104032
%N A017981 Powers of cube root of 2 rounded up.
%H A017981 Vincenzo Librandi, <a href="/A017981/b017981.txt">Table of n, a(n) for n = 0..1000</a>
%t A017981 Table[Ceiling[(2^(1/3))^n], {n, 0, 300}] (* _Vincenzo Librandi_, Jan 05 2014 *)
%o A017981 (PARI) a(n) = ceil(sqrtn(2, 3)^n); \\ _Michel Marcus_, Jan 03 2014
%o A017981 (Python)
%o A017981 def icbrt(a):
%o A017981     sr = 1 << (int.bit_length(int(a)) >> 1)
%o A017981     while a < sr*sr*sr:  sr>>=1
%o A017981     b = sr>>1
%o A017981     while b:
%o A017981       s = sr+b
%o A017981       if a >= s*s*s:  sr = s
%o A017981       b>>=1
%o A017981     return sr
%o A017981 for n in range(100):  print(1+icbrt(2**n-1), end=",")
%o A017981 # _Alex Ratushnyak_, Jan 04 2014
%o A017981 (Magma) [Ceiling(2^(n/3)): n in [1..60]]; // _Vincenzo Librandi_, Jan 05 2014
%Y A017981 Cf. A017979.
%K A017981 nonn
%O A017981 0,2
%A A017981 _N. J. A. Sloane_
%E A017981 a(44)-a(50) from _Alex Ratushnyak_, Jan 02 2014