A396786 Smallest prime p such that p^(q^3) = +-1 mod q^5 is true when q is any of the first n primes.

3, 17, 199, 22051, 387199, 52246349, 3753373051, 3884699495951

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Rhys Feltman, Python code

Example

a(1) = 3 because 3^(2^3) mod 2^5 = +-1: 3^8 = 6561. 6561 = 205*32 (6560) + 1. Prime 2 obviously does not work because 2^m mod 2^n will always be either 0 or 2^m.

Prog

(PARI) isok(p, vp) = for (i=1, #vp, my(q=vp[i], q5=q^5, m=Mod(p, q5)^q^3); if ((m != Mod(1, q5)) && (m != Mod(-1, q5)), return(0)); ); 1;
a(n) = my(p=2, vp=primes(n)); while (!isok(p, vp), p=nextprime(p+1)); p; \\ Michel Marcus, Jun 13 2026

Crossrefs

Cf. A395587 (with q^2 instead of q^3).

Sequence in context: A335343 A133991 A210898 * A009494 A267659 A075271

Adjacent sequences: A396781 A396784 A396785 * A396787 A396788 A396789

Keyword

nonn,more,changed

Author

Rhys Feltman, Jun 05 2026

Extensions

a(6) from Michel Marcus, Jun 13 2026

a(7)-a(8) from Max Alekseyev, Jul 15 2026

Status

approved