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A018852 a(n)^3 is smallest cube beginning with n.

%I A018852 #38 Apr 30 2020 13:38:37
%S A018852 0,1,3,7,16,8,4,9,2,21,10,48,5,11,52,25,55,12,57,27,59,6,61,62,29,63,
%T A018852 64,3,66,31,67,68,32,15,7,33,154,72,73,34,16,161,35,76,164,77,36,78,
%U A018852 169,17,37,8,174,81,38,82,178,83,18,39,182,85,184,86,4,87,188,189,19,191,89,193,9
%N A018852 a(n)^3 is smallest cube beginning with n.
%H A018852 Seiichi Manyama, <a href="/A018852/b018852.txt">Table of n, a(n) for n = 0..10000</a> (terms 1..1000 from T. D. Noe)
%F A018852 a(n) >= n^(1/3), for all n > 0, with equality when n is a cube. - _Derek Orr_, Jul 26 2015
%p A018852 f:= proc(n) local d,m;
%p A018852   for d from 0 do
%p A018852     m:= ceil((10^d*n)^(1/3));
%p A018852     if m^3 < 10^d*(n+1) then return m fi
%p A018852   od
%p A018852 end proc:
%p A018852 map(f, [$1..100]); # _Robert Israel_, Jul 26 2015
%o A018852 (Python)
%o A018852 for n in range(1,10**3):
%o A018852     for k in range(10**3):
%o A018852         if str(k**3).startswith(str(n)):
%o A018852             print(k,end=', ')
%o A018852             break
%o A018852     n += 1 # _Derek Orr_, Aug 03 2014
%o A018852 (PARI) a(n)=k=1;while(k,d=digits(k^3);D=digits(n);if(#D<=#d,c=1;for(i=1,#D,if(D[i]!=d[i],c=0;break));if(c,return(k)));k++)
%o A018852 vector(100,n,a(n)) \\ _Derek Orr_, Jul 26 2015
%Y A018852 Cf. A018797.
%Y A018852 Cf. A018851 (k=2), this sequence (k=3), A018853 (k=4), A018872 (k=5), A018874 (k=6), A018876 (k=7), A018878 (k=8), A018880 (k=9), A018882 (k=10).
%K A018852 nonn,base,look
%O A018852 0,3
%A A018852 _David W. Wilson_
%E A018852 0 prepended by _Seiichi Manyama_, Jan 30 2017