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 1-8 of 8 results.

A159991 Powers of 60: a(n) = 60^n.

Original entry on oeis.org

1, 60, 3600, 216000, 12960000, 777600000, 46656000000, 2799360000000, 167961600000000, 10077696000000000, 604661760000000000, 36279705600000000000, 2176782336000000000000, 130606940160000000000000, 7836416409600000000000000, 470184984576000000000000000
Offset: 0

Views

Author

Reinhard Zumkeller, May 01 2009

Keywords

Examples

			G.f. = 1 + 60*x + 3600*x^2 + 216000*x^3 + 12960000*x^4 + 77600000*x^5 + ... - _Michael Somos_, Jan 01 2019

Links

Crossrefs

Subsequence of A051037.
Cf. A159990, A159993, A159995, A088157, A091649, A125628, A091720, A091721, A091722, A060707, A070197.

Programs

Formula

a(n) = A000400(n)*A011557(n) = A000351(n)*A001021(n) = A000302(n)*A001024(n) = A000244(n)*A009964(n). (Corrected by Robert B Fowler, Jan 25 2023)
From Muniru A Asiru, Nov 21 2018: (Start)
a(n) = 60^n.
a(n) = 60*a(n-1) for n > 0, a(0) = 1.
G.f.: 1/(1-60*x).
E.g.f: exp(60*x). (End)
a(n) = 1/a(-n) for all n in Z. - Michael Somos, Jan 01 2019

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.

A088153 a(n) is the value of the n-th digit in the decimal representation of n^n.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

Comments

a(n) = d(n) with n^n = Sum_{0<=d(k)<10, k>=0} d(k)*10^k.

Examples

			For n=16, 16^16 = 18446744073709551616, a(16)=4.
a(0)=1, a(k)=0 for 0 < k < 10 and a(10)=1.

Links

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088154, A088155, A088156, A088157.

Programs

  • Maple
    f:= proc(n) local x, L;
   x:= n &^ n mod 10^(n+1);
   floor(x/10^n)
end proc:
f(0):= 1:
map(f, [$0..101]); # Robert Israel, Dec 02 2022

Formula

a(n) = floor(n^n / 10^n) mod 10.

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 1-8 of 8 results.

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