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 1-7 of 7 results.

A088157 Value of (n+1)-th digit in sexagesimal representation of n^n.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 7, 21, 2, 1, 59, 5, 49, 2, 19, 57, 20, 45, 35, 30, 0, 5, 28, 50, 4, 19, 50, 23, 32, 10, 23, 38, 16, 45, 29, 6
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n) = d(n) with n^n = Sum(d(k)*60^k: 0 <= d(k) < 60, k >= 0).

Examples

			a(0) = 1, a(k) = 0 for 0 < k < 60 and a(60) = 1.

Links

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088153, A088154, A088155, A088156, A159991.

Programs

  • Haskell
    a088157 n = mod (div (n ^ n) (60 ^ n)) 60
-- Reinhard Zumkeller, Mar 14 2014
  • Mathematica
    f[n_] := IntegerDigits[n^n, 60, n + 1][[1]]; f[0] = 1; Array[f, 92, 0] (* Robert G. Wilson v, Dec 27 2012 *)
  • PARI
    a(n)=lift(chinese(chinese(Mod(n,3^(n+1))^n,Mod(n,4^(n+1))^n), Mod(n,5^(n+1))^n))\60^n \\ Charles R Greathouse IV, Dec 27 2012

Formula

a(n) = floor(n^n / 60^n) mod 60.

A088152 Value of n-th digit in octal representation of n^n.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 6, 6, 5, 0, 0, 4, 4, 6, 1, 3, 3, 1, 4, 5, 4, 0, 5, 0, 3, 0, 3, 4, 1, 3, 5, 6, 2, 1, 6, 6, 5, 5, 0, 1, 0, 0, 5, 6, 3, 7, 6, 4, 1, 1, 3, 3, 6, 4, 3, 1, 0, 0, 0, 4, 4, 0, 3, 6, 1, 1, 2, 5, 0, 0, 5, 2, 6, 0, 2, 4, 7, 5, 6, 4, 2, 1, 6, 4, 3, 6, 7, 4, 6, 0, 5, 7, 5, 3, 6
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*8^k: 0<=d(k)<8, k>=0).

Examples

			n=9, 9^9=387420489 -> '2705710511', '2---------': a(9)=2;
a(0)=1, a(k)=0 for 0<k<8 and a(8)=1.

Links

Crossrefs

Cf. A007094, A000312, A088150, A088151, A088153, A088154, A088155, A088156, A088157.

Programs

  • Magma
    [Floor(n^n/8^n) mod 8:n in [0..101]]; // Marius A. Burtea, Sep 20 2019
  • Maple
    f:= proc(n) local x,L;
   x:= n &^ n mod 8^(n+1);
   floor(x/8^n)
end proc:
f(0):= 1:
map(f, [$0..101]); # Robert Israel, Sep 19 2019

Formula

a(n) = floor(n^n / 8^n) mod 8.

A088150 Value of n-th digit (counting from the right) in binary representation of n^n.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*2^k: 0<=d(k)<2, k>=0).

Examples

			n=5, 5^5=3125 -> '110000110101', '1100001-----': a(5)=1.

Links

  • Eric Weisstein's World of Mathematics, Binary

Crossrefs

Cf. A007088, A000312, A088151, A088152, A088153, A088154, A088155, A088156, A088157.

Programs

  • Mathematica
    Join[{1,0},Table[IntegerDigits[n^n,2][[-n-1]],{n,2,110}]] (* Harvey P. Dale, Oct 14 2021 *)

Formula

a(n) = floor(n^n / 2^n) mod 2.

Extensions

Definition clarified by Harvey P. Dale, Oct 14 2021

A088151 Value of n-th digit in ternary representation of n^n.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 0, 1, 1
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*3^k: 0<=d(k)<3, k>=0).

Examples

			n=7, 7^7=3110367 -> '1112211200121', '111221-------': a(7)=1.

Links

  • Eric Weisstein's World of Mathematics, Ternary

Crossrefs

Cf. A007089, A000312, A088150, A088152, A088153, A088154, A088155, A088156, A088157.

Formula

a(n) = floor(n^n / 3^n) mod 3.

A088154 Value of n-th digit in duodecimal representation of n^n.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 4, 3, 0, 1, 0, 3, 2, 3, 9, 4, 7, 5, 4, 3, 7, 4, 6, 5, 4, 10, 4, 9, 1, 7, 5, 4, 8, 4, 11, 2, 4, 0, 8, 4, 10, 7, 6, 5, 8, 6, 9, 3, 1, 8, 7, 1, 6, 0, 8, 8, 2, 1, 8, 1, 5, 10, 0, 0, 6, 5, 10, 11, 11, 7, 7, 1, 10, 2, 3, 1, 0, 4, 10, 8, 5, 7, 6, 11, 2, 6, 1, 4, 0
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*12^k: 0<=d(k)<12, k>=0).

Examples

			n=16, 16^16=18446744073709551616 -> [839365134A210240714], a(16)=3.
a(0)=1, a(k)=0 for 0<k<12 and a(12)=1.

Links

  • Eric Weisstein's World of Mathematics, Duodecimal

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088153, A088155, A088156, A088157.

Programs

  • Mathematica
    Join[{1},Table[Mod[Floor[n^n/12^n],12],{n,100}]] (* Harvey P. Dale, Apr 17 2012 *)

Formula

a(n) = floor(n^n / 12^n) mod 12.

A088155 Value of n-th digit in hexadecimal representation of n^n.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 10, 6, 14, 15, 8, 2, 0, 0, 13, 11, 5, 8, 6, 0, 12, 6, 0, 12, 1, 11, 2, 4, 11, 11, 3, 15, 8, 4, 10, 1, 14, 1, 14, 0, 6, 0, 5, 14, 12, 9, 9, 1, 4, 2, 1, 0, 10, 7, 15, 4, 10, 15, 3, 13, 1, 12, 7, 15, 14, 4, 7, 1, 14, 8, 5, 8, 4, 9, 9, 13, 6
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*16^k: 0<=d(k)<16, k>=0).

Examples

			n=20, 20^20=1048576*10^20 -> [56BC75E2D6310000000000], a(20)=6.
a(0)=1, a(k)=0 for 0<k<16 and a(16)=1.

Links

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088153, A088154, A088156, A088157.

Formula

a(n) = floor(n^n / 16^n) mod 16.

A088156 Value of n-th digit in vigesimal representation of n^n.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 4, 19, 4, 17, 3, 7, 6, 11, 5, 3, 6, 5, 13, 8, 15, 19, 4, 16, 2, 12, 5, 5, 9, 6, 5, 9, 17, 1, 14, 11, 10, 15, 15, 13, 2, 8, 9, 1, 18, 3, 15, 15, 17, 10, 1, 5, 0, 3, 16, 4, 17, 14, 12, 12, 6, 5, 8, 16, 8, 3, 6, 12, 19, 2, 14
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n)=d(n) with n^n = Sum(d(k)*20^k: 0<=d(k)<20, k>=0).

Examples

			n=30, 30^30=205891132094649*10^30 -> [93B83A81A7CBBA03C2241239C3C4840000000], a(30)=8.
a(0)=1, a(k)=0 for 0<k<20 and a(20)=1.

Links

  • Eric Weisstein's World of Mathematics, Vigesimal

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088153, A088154, A088155, A088157.

Formula

a(n) = floor(n^n / 20^n) mod 20.
Showing 1-7 of 7 results.

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