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a(n)^3 is smallest cube beginning with n.
13

%I #38 Apr 30 2020 13:38:37

%S 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 64,3,66,31,67,68,32,15,7,33,154,72,73,34,16,161,35,76,164,77,36,78,

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

%H 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 a(n) >= n^(1/3), for all n > 0, with equality when n is a cube. - _Derek Orr_, Jul 26 2015

%p f:= proc(n) local d,m;

%p for d from 0 do

%p m:= ceil((10^d*n)^(1/3));

%p if m^3 < 10^d*(n+1) then return m fi

%p od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jul 26 2015

%o (Python)

%o for n in range(1,10**3):

%o for k in range(10**3):

%o if str(k**3).startswith(str(n)):

%o print(k,end=', ')

%o break

%o n += 1 # _Derek Orr_, Aug 03 2014

%o (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 vector(100,n,a(n)) \\ _Derek Orr_, Jul 26 2015

%Y Cf. A018797.

%Y 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 nonn,base,look

%O 0,3

%A _David W. Wilson_

%E 0 prepended by _Seiichi Manyama_, Jan 30 2017