A018852 -id:A018852 - cp's OEIS frontend

A018853 a(n)^4 is smallest fourth power beginning with n.

0, 1, 4, 14, 8, 15, 5, 29, 3, 31, 10, 33, 6, 19, 11, 35, 2, 65, 37, 21, 12, 68, 69, 22, 7, 4, 72, 23, 13, 74, 132, 42, 134, 24, 43, 77, 138, 44, 14, 25, 8, 45, 144, 81, 46, 26, 147, 83, 47, 84, 15, 151, 85, 27, 86, 273, 154, 49, 276, 88, 157, 28, 5, 159, 283, 9, 286, 51, 91, 289, 29

Offset: 0

David W. Wilson

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018798 (a(n)^4).

Cf. A018851 (k=2), A018852 (k=3), this sequence (k=4), A018872 (k=5), A018874 (k=6), A018876 (k=7), A018878 (k=8), A018880 (k=9), A018882 (k=10).

v=[]; k=1; while(#v<100, d=digits(k^4); D=digits(#v+1); if(#D<=#d, c=1; for(i=1, #D, if(D[i]!=d[i], c=0; break)); if(c, v=concat(v, k); k=0)); k++); v \\ Derek Orr, Aug 12 2015

a(n^4) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018872 a(n)^5 is smallest fifth power beginning with n.

Original entry on oeis.org

0, 1, 3, 2, 21, 9, 23, 6, 61, 25, 4, 26, 66, 42, 17, 69, 7, 28, 18, 72, 29, 116, 47, 75, 3, 48, 192, 77, 31, 124, 79, 5, 2, 32, 51, 129, 205, 13, 52, 33, 21, 53, 212, 134, 85, 34, 136, 86, 137, 87, 55, 22, 35, 14, 352, 56, 224, 142, 226, 9, 36, 144, 91, 363, 23, 58, 146, 232, 147, 37

Offset: 0

David W. Wilson

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), this sequence (k=5), A018874 (k=6), A018876 (k=7), A018878 (k=8), A018880 (k=9), A018882 (k=10).

a(n) = my(k=0, ss=Str(n)); while(strsplit(Str(k^5), ss)[1] != "", k++); k; \\ Michel Marcus, Aug 19 2025

a(n^5) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018874 a(n)^6 is smallest sixth power beginning with n.

Original entry on oeis.org

0, 1, 8, 18, 4, 9, 2, 3, 21, 46, 10, 7, 33, 49, 23, 5, 16, 11, 35, 24, 77, 36, 53, 115, 17, 37, 8, 55, 81, 12, 26, 121, 83, 263, 18, 39, 124, 85, 27, 271, 4, 127, 59, 87, 188, 189, 6, 19, 13, 89, 131, 61, 132, 9, 42, 133, 62, 134, 197, 29, 92, 292, 63, 43, 2, 201, 137, 202, 64, 138

Offset: 0

David W. Wilson

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), A018872 (k=5), this sequence (k=6), A018876 (k=7), A018878 (k=8), A018880 (k=9), A018882 (k=10).

a(n^6) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018876 a(n)^7 is smallest seventh power beginning with n.

Original entry on oeis.org

0, 1, 3, 12, 9, 34, 13, 5, 7, 37, 10, 38, 2, 28, 76, 55, 4, 15, 21, 11, 8, 3, 58, 42, 22, 114, 16, 6, 116, 84, 117, 44, 85, 119, 23, 12, 167, 45, 234, 63, 88, 17, 33, 46, 89, 24, 173, 9, 174, 65, 47, 91, 34, 127, 66, 92, 128, 248, 48, 129, 67, 18, 13, 181, 35, 351, 131, 49, 183, 95, 255

Offset: 0

David W. Wilson

			a(2)=3, because 3^7=2187 is the first 7th power with the most significant digit 2;
a(16)=4, because 4^7=16384 is the first 7th power whose two most significant digits are 16.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), A018872 (k=5), A018874 (k=6), this sequence (k=7), A018878 (k=8), A018880 (k=9), A018882 (k=10).

a(n^7) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018878 a(n)^8 is smallest eighth power beginning with n.

Original entry on oeis.org

0, 1, 2, 5, 9, 7, 3, 23, 13, 42, 10, 18, 58, 78, 14, 25, 6, 34, 81, 61, 26, 11, 35, 47, 63, 2, 113, 85, 27, 86, 115, 65, 87, 49, 277, 37, 66, 21, 158, 5, 67, 283, 12, 9, 286, 51, 287, 91, 289, 122, 29, 69, 123, 39, 22, 93, 221, 7, 222, 125, 94, 223, 53, 126, 71, 3, 95, 127, 226, 17

Offset: 0

David W. Wilson

a(2)=2, because 2^8=256 is the first 8th power with the most significant decimal digit equal to 2;

a(16)=6, because 6^8=1679616 is the first 8th power with two most significant decimal digits equal to 16.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), A018872 (k=5), A018874 (k=6), A018876 (k=7), this sequence (k=8), A018880 (k=9), A018882 (k=10).

a(n^8) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018880 a(n)^9 is smallest ninth power beginning with n.

Original entry on oeis.org

0, 1, 4, 9, 7, 2, 16, 21, 59, 46, 6, 17, 22, 8, 29, 63, 38, 137, 23, 3, 14, 109, 141, 11, 184, 86, 4, 52, 87, 188, 113, 68, 19, 191, 148, 32, 149, 193, 9, 54, 7, 117, 91, 152, 118, 71, 33, 92, 154, 332, 43, 2, 93, 201, 26, 121, 261, 94, 73, 122, 34, 44, 264, 57, 123, 343, 74, 344, 16

Offset: 0

David W. Wilson

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), A018872 (k=5), A018874 (k=6), A018876 (k=7), A018878 (k=8), this sequence (k=9), A018882 (k=10).

a(n^9) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018882 a(n)^10 is smallest tenth power beginning with n.

Original entry on oeis.org

0, 1, 7, 9, 23, 3, 6, 49, 31, 5, 2, 32, 81, 13, 26, 33, 21, 42, 67, 85, 17, 43, 86, 109, 69, 11, 22, 35, 7, 28, 56, 89, 71, 113, 9, 18, 36, 72, 91, 182, 115, 23, 29, 58, 116, 232, 185, 147, 37, 74, 148, 59, 47, 94, 375, 188, 75, 15, 189, 3, 6, 12, 38, 24, 48, 152, 96, 121, 192, 305

Offset: 0

David W. Wilson

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A018851 (k=2), A018852 (k=3), A018853 (k=4), A018872 (k=5), A018874 (k=6), A018876 (k=7), A018878 (k=8), A018880 (k=9), this sequence (k=10).

a(n^10) = n for n >= 0. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A018797 Smallest cube that begins with n.

Original entry on oeis.org

0, 1, 27, 343, 4096, 512, 64, 729, 8, 9261, 1000, 110592, 125, 1331, 140608, 15625, 166375, 1728, 185193, 19683, 205379, 216, 226981, 238328, 24389, 250047, 262144, 27, 287496, 29791, 300763, 314432, 32768, 3375, 343, 35937, 3652264, 373248

Offset: 0

David W. Wilson

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

Cf. A018852, A018796.

a[n_] := For[idn = IntegerDigits[n]; k = 1, True, k++, idk = IntegerDigits[k^3]; If[Length[idn] <= Length[idk], If[idk[[1 ;; Length[idn]]] == idn, Return[k^3]]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 1000}] (* Jean-François Alcover, Mar 13 2016 *)
id[n_]:=With[{idn=IntegerDigits[n]},idn==Take[IntegerDigits[#], Length[ idn]]&]; With[{c=Range[0,250]^3},Table[SelectFirst[c,id[k]],{k,0,40}]]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 08 2018 *)

for n in range(1, 10**3):
  for k in range(10**3):
    if str(k**3).startswith(str(n)):
      print(k**3, end=', ')
      break
  n += 1 # Derek Orr, Aug 03 2014

a(n) = A018852(n)^3. - Seiichi Manyama, Jan 30 2017

Added initial 0. - Seiichi Manyama, Jan 30 2017

A030669 Cube root of A030668.

Original entry on oeis.org

5, 3, 7, 16, 8, 4, 9, 20, 21, 10, 48, 5, 11, 52, 25, 55, 12, 57, 27, 59, 6, 61, 62, 29, 63, 64, 14, 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, 40, 87, 188

Offset: 1

Patrick De Geest

a(n) = A018852(n) if n is not a cube. - Robert Israel, Dec 25 2018

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A018852, A030668.

f:= proc(n) local d,x;
  for d from 1 do
    x:= ceil((n*10^d)^(1/3));
    if x^3 < (n+1)*10^d then return x fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 25 2018

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).

cp's OEIS Frontend

A018853 a(n)^4 is smallest fourth power beginning with n.

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A018872 a(n)^5 is smallest fifth power beginning with n.

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A018874 a(n)^6 is smallest sixth power beginning with n.

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A018876 a(n)^7 is smallest seventh power beginning with n.

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A018878 a(n)^8 is smallest eighth power beginning with n.

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A018880 a(n)^9 is smallest ninth power beginning with n.

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A018882 a(n)^10 is smallest tenth power beginning with n.

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A018797 Smallest cube that begins with n.

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A030669 Cube root of A030668.

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