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

%I A175348 #24 Mar 24 2024 18:20:10
%S A175348 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 A175348 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 A175348 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 A175348 Last digit of p^p, where p is the n-th prime.
%C A175348 Euler and Sadek ask whether the sequence, interpreted as the decimal expansion N = 0.47531..., is rational or irrational.
%C A175348 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 A175348 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 A175348 Robert Israel, <a href="/A175348/b175348.txt">Table of n, a(n) for n = 1..10000</a>
%F A175348 a(n) = A056849(A000040(n)). - _Robert Israel_, Jan 26 2017
%e A175348 prime(4) = 7 and 7^7 = 823543, so a(4) = 3.
%p A175348 R:= [seq(i &^ i mod 10, i=1..20)]:
%p A175348 seq(R[ithprime(i) mod 20],i=1..100); # _Robert Israel_, Jan 26 2017
%t A175348 Table[PowerMod[n,n,10],{n,Prime[Range[110]]}] (* _Harvey P. Dale_, Mar 24 2024 *)
%o A175348 (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 A175348 Cf. A000040, A007652, A056849, A137807.
%K A175348 base,easy,nonn
%O A175348 1,1
%A A175348 _Charles R Greathouse IV_, Apr 19 2010