A175348 Last digit of p^p, where p is the n-th prime.

4, 7, 5, 3, 1, 3, 7, 9, 7, 9, 1, 7, 1, 7, 3, 3, 9, 1, 3, 1, 3, 9, 7, 9, 7, 1, 7, 3, 9, 3, 3, 1, 7, 9, 9, 1, 7, 7, 3, 3, 9, 1, 1, 3, 7, 9, 1, 7, 3, 9, 3, 9, 1, 1, 7, 7, 9, 1, 7, 1, 7, 3, 3, 1, 3, 7, 1, 7, 3, 9, 3, 9, 3, 3, 9, 7, 9, 7, 1, 9, 9, 1, 1, 3, 9, 7, 9, 7, 1, 7, 3, 9, 3, 1, 9, 7, 9, 1, 7, 1, 3, 7, 7, 9, 1

Offset: 1

Author

Charles R Greathouse IV, Apr 19 2010

Keywords

• base
• easy
• nonn

Comments

Euler and Sadek ask whether the sequence, interpreted as the decimal expansion N = 0.47531..., is rational or irrational.

Dickson's conjecture implies that each finite sequence with values in {1,3,7,9} occurs as a substring. In particular, this implies that the above N is irrational. - Robert Israel, Jan 26 2017

Examples

			prime(4) = 7 and 7^7 = 823543, so a(4) = 3.
		

References

• R. Euler and J. Sadek, A number that gives the unit digit of n^n. Journal of Recreational Mathematics, 29:3 (1998), pp. 203-204.

Links

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

Crossrefs

Cf. A000040, A007652, A056849, A137807.

Programs

Maple

R:= [seq(i &^ i mod 10, i=1..20)]:
seq(R[ithprime(i) mod 20],i=1..100); # Robert Israel, Jan 26 2017

Mathematica

Table[PowerMod[n,n,10],{n,Prime[Range[110]]}] (* Harvey P. Dale, Mar 24 2024 *)

PARI

a(n)=[1,4,7,0,5,0,3,0,9,0,1,0,3,0,0,0,7,0,9][prime(n)%20]

Formula

a(n) = A056849(A000040(n)). - Robert Israel, Jan 26 2017