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%I #6 Mar 04 2020 07:37:58
%S 0,1,0,1,4,3,1,1,0,9,5,9,1,1,9,9,9,9,1,9,15,5,8,9,14,1,0,1,9,9,4,9,27,
%T 9,29,9,1,1,27,9,9,15,11,5,9,31,32,9,15,39,9,1,9,27,49,1,39,9,57,9,34,
%U 35,36,9,14,27,22,9,54,29,12,9,72,1,39,1,71,27
%N Tower of 9's modulo n.
%C a(n) = (9^(9^(9^(9^ ... )))) mod n, provided sufficient 9's are in the tower such that adding more doesn't affect the value of a(n).
%F a(n) = 9^a(A000010(n)) mod n.
%F a(n) = (9^^k) mod n, if n < A246497(k), where ^^ is Knuth's double-arrow notation.
%o (PARI) a(n) = {my(b, c=0, d=n, k=1, x=1); while(k==1, z=x; y=1; b=1; while(z>0, while(y<z, d=eulerphi(d); y++); b=9^b-floor((9^b-1)/d)*d; z=z-1; y=1; d=n); if(c==b, k=0); c=b; x++); b%n; }
%Y Cf. A240162, A245970, A245971, A245972, A245973, A245974, A246497, A332055.
%K nonn
%O 1,5
%A _Jinyuan Wang_, Mar 03 2020
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