A056849 -id:A056849 - cp's OEIS frontend

A365936 Final digit (in decimal system) of n^(n-1) = A000169(n).

1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9

Offset: 1

Marco Ripà, Sep 23 2023

This is a periodic sequence with period 20 which is twice the considered radix.

			For n = 4, a(4) = 4^3 mod 10 = 64 mod 10 = 4.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A000169, A056849, A120962, A138029, A365707.

a[n_]:=Last[IntegerDigits[n^(n-1)]]; Array[a,87] (* Stefano Spezia, Sep 26 2023 *)

a(n) = n^(n-1) mod 10.

a(n) = A365935(n+10).

A143959 Final digit of n^(n+1)-(n+1)^n for n>2.

Original entry on oeis.org

7, 9, 9, 7, 9, 7, 1, 9, 3, 1, 5, 9, 9, 5, 1, 1, 1, 9, 9, 9, 7, 9, 9, 7, 9, 7, 1, 9, 3, 1, 5, 9, 9, 5, 1, 1, 1, 9, 9, 9, 7, 9, 9, 7, 9, 7, 1, 9, 3, 1, 5, 9, 9, 5, 1, 1, 1, 9, 9, 9, 7, 9, 9, 7, 9, 7, 1, 9, 3, 1, 5, 9, 9, 5, 1, 1, 1, 9, 9, 9, 7, 9, 9, 7, 9, 7, 1, 9, 3, 1, 5, 9, 9, 5, 1, 1, 1, 9, 9, 9

Offset: 3

Sébastien Dumortier, Sep 05 2008

Cyclic with a period of 20

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

A056849

Last[IntegerDigits[#^(#+1)-(#+1)^#]]&/@ Range[3,150]  (* Harvey P. Dale, Mar 12 2011 *)

# -*- coding: iso-8859-1 -*- from math import * n=3 while n<100: ....r=(n**(n+1)-(n+1)**n)%10 ....print r, ....n=n+1

A209466 Final digit of n^n - n.

Original entry on oeis.org

1, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0

Offset: 0

Radu Borza, Mar 09 2012

Note: cyclic with a period of 20 for n > 0.

R. Euler & J. Sadek, "A number that gives the units of n^n", Journal of Recreational Mathematics 29:3 (1998), pp. 203-204.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A056849.

Maple
```
[seq((n^n-n) mod 10, n=1..40)];
```

Join[{1}, Table[Mod[PowerMod[n, n, 10] - n, 10], {n, 100}]] (* T. D. Noe, Mar 13 2012 *)
PadRight[{1},120,{0,0,2,4,2,0,0,6,8,0,0,0,4,0,2,0,0,0,6,0}] (* Harvey P. Dale, May 21 2020 *)

a(n)=lift(Mod(n,10)^n-n) \\ Charles R Greathouse IV, Mar 13 2012

Perl
```
print (($**$-$_)%10) for (1..40);
```

a(n) = (n^n-n) mod 10

A309697 a(n) is the digit that precedes the last nonzero digit of n^n.

Original entry on oeis.org

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

Offset: 1

Michel Marcus, Aug 13 2019

Chu proves that the constant 0.00252541801... is transcendental.

Hung Viet Chu, New Transcendental Numbers from Certain Sequences, arXiv:1908.03855 [math.NT], 2019.

Cf. A056849.

a[n_] := Floor[PowerMod[n/10^IntegerExponent[n, 10], n, 100]/10]; Array[a, 100] (* Giovanni Resta, Aug 13 2019 *)

a(n) = {my(d=digits(n^n)); forstep (k=#d, 1, -1, if (d[k], if (k==1, return (0)); return (d[k-1]));); return(0);}

A347671 a(n) = n^n mod 100.

Original entry on oeis.org

1, 1, 4, 27, 56, 25, 56, 43, 16, 89, 0, 11, 56, 53, 16, 75, 16, 77, 24, 79, 0, 21, 84, 67, 76, 25, 76, 3, 36, 69, 0, 31, 76, 13, 36, 75, 36, 17, 4, 59, 0, 41, 64, 7, 96, 25, 96, 63, 56, 49, 0, 51, 96, 73, 56, 75, 56, 57, 84, 39, 0, 61, 44, 47, 16, 25, 16, 23

Offset: 0

John Bibby, Sep 10 2021

Index entries for linear recurrences with constant coefficients, signature (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, 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).

Cf. A000312 (n^n), A056849 (mod 10), A174824.

Table[PowerMod[n,n,100],{n,0,70}] (* Harvey P. Dale, Aug 13 2023 *)

def a(n): return pow(n, n, 100)
print([a(n) for n in range(101)]) # Michael S. Branicky, Sep 26 2021

For n >= 101, a(n) = a(n-100), i.e., cyclic with period A174824(100) = 100, disregarding a(0). - Michael S. Branicky, Sep 26 2021

cp's OEIS Frontend

A365936 Final digit (in decimal system) of n^(n-1) = A000169(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A143959 Final digit of n^(n+1)-(n+1)^n for n>2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A209466 Final digit of n^n - n.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Perl

Formula

A309697 a(n) is the digit that precedes the last nonzero digit of n^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A347671 a(n) = n^n mod 100.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Formula