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

1,3

Comments

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

Links

Table of n, a(n) for n=1..76.

Example

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

Prog

(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)) )) }

Crossrefs

Cf. A000040.

Sequence in context: A292108 A352910 A362328 * A325195 A026728 A241556

Adjacent sequences: A342173 A342174 A342175 * A342177 A342178 A342179

Keyword

nonn

Author

Peter Schorn, Mar 04 2021

Status

approved