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A175348
Last digit of p^p, where p is the n-th 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
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. 203-204.
LINKS
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
MATHEMATICA
Table[PowerMod[n, n, 10], {n, Prime[Range[110]]}] (* Harvey P. Dale, Mar 24 2024 *)
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
KEYWORD
base,easy,nonn
AUTHOR
STATUS
approved