cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A067444 Smallest n-th power starting with 3.

Original entry on oeis.org

3, 36, 343, 38416, 32, 34012224, 35831808, 390625, 387420489, 3486784401, 362797056, 3138428376721, 34522712143931, 379749833583241, 32768, 33232930569601, 30491346729331195904, 387420489, 319479999370622926848
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443.

Programs

  • Maple
    f:= proc(n) local k,x;
  for k from 0 do
    x:= ceil((3*10^k)^(1/n))^n;
    if x < 4*10^k then return x fi
  od
end proc:
map(f, [$1..30]); # Robert Israel, Feb 12 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 3, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067445 Smallest n-th power starting with 4.

Original entry on oeis.org

4, 4, 4096, 4096, 4084101, 4096, 4782969, 43046721, 40353607, 41426511213649, 4194304, 4096, 4503599627370496, 4782969, 470184984576, 43046721, 456487940826035155404146917, 426878854210636742656, 4394336169668803158610484050361, 4064231406647572522401601
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 4 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 4, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

Extensions

Moved Mathematica program to proper field -- Harvey P. Dale, Mar 31 2012

A067446 Smallest n-th power starting with 5.

Original entry on oeis.org

5, 529, 512, 50625, 59049, 531441, 52523350144, 5764801, 512, 59049, 584318301411328, 531441, 549755813888, 53148384174432398229504, 51185893014090757, 5070942774902496337890625, 505447028499293771
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 5 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 5, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067447 Smallest n-th power starting with 6.

Original entry on oeis.org

6, 64, 64, 625, 6436343, 64, 62748517, 6561, 68719476736, 60466176, 64268410079232, 68719476736, 67108864, 6103515625, 6746640616477458432, 65536, 66249952919459433152512, 68719476736, 609359740010496
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445, A067446.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 6 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 6, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067448 Smallest n-th power whose decimal expansion starts with 7.

Original entry on oeis.org

7, 729, 729, 707281, 7776, 729, 78125, 78310985281, 794280046581, 79792266297612001, 743008370688, 7355827511386641, 793714773254144, 78364164096, 734461618571137961752599, 79766443076872509863361
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445, A067446, A067447.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 7 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 7, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067449 Smallest n-th power starting with 8.

Original entry on oeis.org

8, 81, 8, 81, 844596301, 85766121, 823543, 815730721, 8662995818654939, 819628286980801, 8589934592, 8916100448256, 8192, 805345924720991301978201, 8629188747598184440949
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445, A067446, A067447, A067448.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 8 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 8, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067450 Smallest n-th power starting with 9.

Original entry on oeis.org

9, 9, 9261, 923521, 9765625, 9474296896, 94931877133, 9682651996416, 922190162669056, 9765625, 952809757913927, 95428956661682176, 96889010407, 9012061295995008299689, 931322574615478515625
Offset: 1

Views

Author

Amarnath Murthy, Feb 05 2002

Keywords

Comments

Terms from Robert G. Wilson v.

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445, A067446, A067447, A067448, A067449.

Programs

  • Maple
    f:= proc(n) local x, y;
  for x from 2 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 9 then return x^n fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Apr 02 2025
  • Mathematica
    a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 9, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* Robert G. Wilson v *)

A067457 Smallest n-th power starting with n.

Original entry on oeis.org

1, 25, 343, 4096, 59049, 64, 78125, 815730721, 922190162669056, 1024, 116490258898219, 129746337890625, 13060694016, 147653612273582215982104576, 15407021574586368, 16400152899115243850138976256, 17179869184
Offset: 1

Views

Author

Amarnath Murthy, Feb 07 2002

Keywords

Links

Crossrefs

Cf. A067442, A067443, A067444, A067445, A067446, A067447, A067448, A067449, A067450, A068001.

Programs

  • Mathematica
    Do[k = Floor[ Log[ 10, n] + 1]; While[ FromDigits[ Take[ IntegerDigits [k^n], Floor[ Log[ 10, n] + 1]]] != n, k++ ]; Print[k^n], {n, 1, 20} ]

Extensions

Edited and extended by Robert G. Wilson v, Feb 08 2002

A309735 a(n) is the least positive integer k such that k^n starts with 2.

Original entry on oeis.org

2, 5, 3, 4, 3, 8, 3, 2, 4, 7, 2, 5, 9, 4, 9, 6, 7, 2, 4, 21, 2, 5, 7, 3, 5, 3, 8, 2, 4, 3, 2, 5, 11, 4, 5, 7, 8, 2, 6, 23, 2, 5, 6, 14, 3, 16, 3, 2, 3, 14, 2, 4, 15, 17, 5, 7, 4, 2, 11, 18, 2, 4, 47, 14, 5, 6, 4, 2, 7, 3, 2, 3, 13, 3, 5, 15, 4, 8, 6, 9, 2, 4, 11, 6, 5, 22, 4
Offset: 1

Views

Author

Robert Israel, Aug 14 2019

Keywords

Comments

For n > 1, take integer d > -n log_10(3^(1/n)-2^(1/n)).
Then 10^(d/n) > 1/(3^(1/n) - 2^(1/n))
so (3*10^d)^(1/n) - (2*10^d)^(1/n) > 1
and therefore a(n) <= ceiling((2*10^d)^(1/n)).
In particular, a(n) always exists.

Examples

			a(5) = 3 because 3^5 = 243 starts with 2, while 1^5=1 and 2^5=32 do not start with 2.

Links

Crossrefs

Cf. A000030, A067443, A309707.

Programs

  • Magma
    m:=1; sol:=[]; for n in [1..100] do k:=2; while Reverse(Intseq(k^n))[1] ne 2 do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Aug 15 2019
  • Maple
    f:= proc(n) local x,y;
  for x from 2  do
    y:= x^n;
      if floor(y/10^ilog10(y)) = 2 then return x fi
  od
end proc:
map(f, [$1..100]);
  • PARI
    a(n) = for(k=1, oo, if(digits(k^n)[1]==2, return(k))) \\ Felix Fröhlich, Aug 14 2019
  • Python
    n = 1
while n < 100:
    k, s = 2, str(2**n)
    while s[0] != "2":
        k = k+1
        s = str(k**n)
    print(n,k)
    n = n+1 # A.H.M. Smeets, Aug 14 2019

Formula

a(n) = A067443(n)^(1/n).
A000030(a(n)^n)=2.
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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