

A175348


Last digit of p^p, where p is the nth prime.


1



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
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OFFSET

1,1


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


REFERENCES

R. Euler and J. Sadek, A number that gives the unit digit of n^n. Journal of Recreational Mathematics, 29:3 (1998), pp. 203204.


LINKS

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


FORMULA

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


EXAMPLE

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


MAPLE

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


PROG

(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]


CROSSREFS

Cf. A000040, A007652, A056849, A137807.
Sequence in context: A166530 A011518 A132265 * A335590 A329363 A079356
Adjacent sequences: A175345 A175346 A175347 * A175349 A175350 A175351


KEYWORD

base,easy,nonn


AUTHOR

Charles R Greathouse IV, Apr 19 2010


STATUS

approved



