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

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, 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, 0, 8, 8, 58, 8, 2, 8, 18, 8, 1, 6, 8, 56

Offset: 1

Author

Peter Schorn, Mar 04 2021

Keywords

• nonn

Comments

a(n) = 0 iff n is a power of 2.

Examples

			a(1) = 0 = 2 mod 1. a(2) = 0 = 2^3 mod 2. a(3) = 2 = 2^3^5 = 2^243 = 2 mod 3.
		

Crossrefs

Cf. A000040.

Programs

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)) )) }