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

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

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from T. D. Noe)

Formula

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

Maple

f:= proc(n) local d, m;
  for d from 0 do
    m:= ceil((10^d*n)^(1/3));
    if m^3 < 10^d*(n+1) then return m fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 26 2015

Prog

(Python)
for n in range(1, 10**3):
    for k in range(10**3):
        if str(k**3).startswith(str(n)):
            print(k, end=', ')
            break
    n += 1 # Derek Orr, Aug 03 2014
(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++)
vector(100, n, a(n)) \\ Derek Orr, Jul 26 2015

Crossrefs

Cf. A018797.

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).

Sequence in context: A175878 A180503 A153578 * A260465 A060092 A035283

Adjacent sequences: A018849 A018850 A018851 * A018853 A018854 A018855

Keyword

nonn,base,look

Author

David W. Wilson

Extensions

0 prepended by Seiichi Manyama, Jan 30 2017

Status

approved