A018797 -id:A018797 - cp's OEIS frontend

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

David W. Wilson

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

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).

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

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

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

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

0 prepended by Seiichi Manyama, Jan 30 2017

A138173 a(n) is the smallest m such that m^3 begins with n^2.

Original entry on oeis.org

1, 16, 21, 55, 63, 154, 17, 4, 201, 10, 23, 113, 257, 27, 609, 295, 307, 148, 1535, 342, 164, 1692, 809, 1793, 397, 878, 9, 428, 944, 4482, 987, 1008, 1029, 4872, 107, 2349, 5154, 5247, 2478, 252, 552, 5609, 5697, 5785, 2726, 1284, 2806, 6131, 2885

Offset: 1

Zak Seidov, Mar 05 2008

Differs from A030691.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A030690, A030691, A018852, A018797, A077729, A077730, A138174.

from gmpy2 import iroot
def A138173(n):
    d, nd = 1, n**2
    while True:
        x = iroot(nd-1,3)[0]+1
        if x**3 < nd+d:
            return int(x)
        d *= 10
        nd *= 10 # Chai Wah Wu, May 24 2016

A138173 = lambda n: next(m for m in IntegerRange(1, infinity) if str(m**3).startswith(str(n**2)))
# D. S. McNeil, Dec 12 2010

a(n) = (A138174(n))^(1/3).

A030673 Smallest cube that begins with n-th prime.

Original entry on oeis.org

27, 343, 512, 729, 110592, 1331, 1728, 19683, 238328, 29791, 314432, 373248, 4173281, 438976, 474552, 531441, 59319, 614125, 6751269, 7189057, 7301384, 79507, 830584, 8998912, 97336, 101194696, 103823, 10793861, 1092727, 11390625

Offset: 1

Patrick De Geest

			a(1) = 27 because 27 = 3^3 is the smallest cube beginning (base 10) with prime(1) = 2.
a(2) = 343 because 343 = 7^3 is the smallest cube beginning (base 10) with prime(2) = 3.

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Cf. A000040, A000578, A018797, A030674.

f[n_] := Block[{k, l = Ceiling@ Log[10, Prime@ n], p = IntegerDigits@ Prime@ n}, k = Ceiling[ Prime[n]^(1/3)]; While[ Take[ IntegerDigits[k^3], l] != p, k++ ]; k^3]; Array[f, 31] (* Robert G. Wilson v, May 31 2008 *)

a(n) = A018797(A000040(n)).

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

A138174 a(n) is the smallest cube that begins with n^2.

Original entry on oeis.org

1, 4096, 9261, 166375, 250047, 3652264, 4913, 64, 8120601, 1000, 12167, 1442897, 16974593, 19683, 225866529, 25672375, 28934443, 3241792, 3616805375, 40001688, 4410944, 4843965888, 529475129, 5764224257, 62570773, 676836152

Offset: 1

Zak Seidov, Mar 05 2008

Differs from A030690.

Cf. A030690, A030691, A018852, A018797, A077729, A077730, A138173.

a(n) = (A138173(n))^3.

Corrected by D. S. McNeil, Dec 12 2010

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

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A138173 a(n) is the smallest m such that m^3 begins with n^2.

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A030673 Smallest cube that begins with n-th prime.

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A138174 a(n) is the smallest cube that begins with n^2.

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