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Last digit of p^p, where p is the n-th prime.
1

%I #24 Mar 24 2024 18:20:10

%S 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,

%T 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,

%U 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

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

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

%C 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

%D 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.

%H Robert Israel, <a href="/A175348/b175348.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A056849(A000040(n)). - _Robert Israel_, Jan 26 2017

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

%p R:= [seq(i &^ i mod 10, i=1..20)]:

%p seq(R[ithprime(i) mod 20],i=1..100); # _Robert Israel_, Jan 26 2017

%t Table[PowerMod[n,n,10],{n,Prime[Range[110]]}] (* _Harvey P. Dale_, Mar 24 2024 *)

%o (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]

%Y Cf. A000040, A007652, A056849, A137807.

%K base,easy,nonn

%O 1,1

%A _Charles R Greathouse IV_, Apr 19 2010