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A342176 Tower of primes modulo n: a(n) = (2^3^5^7^ ... ^prime(n)) mod n.

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%I A342176 #8 Mar 18 2021 08:20:03
%S A342176 0,0,2,0,3,2,1,0,8,8,8,8,8,8,8,0,8,8,18,8,8,8,2,8,8,8,26,8,26,8,8,0,8,
%T A342176 8,8,8,6,18,8,8,8,8,32,8,8,2,7,32,29,8,8,8,18,26,8,8,56,26,42,8,8,8,8,
%U A342176 0,8,8,58,8,2,8,18,8,1,6,8,56
%N A342176 Tower of primes modulo n: a(n) = (2^3^5^7^ ... ^prime(n)) mod n.
%C A342176 a(n) = 0 iff n is a power of 2.
%e A342176 a(1) = 0 = 2 mod 1. a(2) = 0 = 2^3 mod 2. a(3) = 2 = 2^3^5 = 2^243 = 2 mod 3.
%o A342176 (PARI) { a(n, m=n, s=2) = local(g); if(s==prime(n), return(n%m)); g=s^valuation(m, s); m\=g; lift(chinese(Mod(0, g), Mod(s, m)^a(n, eulerphi(m), nextprime(s+1)) )) }
%Y A342176 Cf. A000040.
%K A342176 nonn
%O A342176 1,3
%A A342176 _Peter Schorn_, Mar 04 2021