A353941 Smallest b > 1 such that b^(p-1) == 1 (mod p^8) for p = prime(n).

257, 6560, 110443, 2387947, 9236508, 6826318, 112184244, 674273372, 571782680, 8827420195, 46142113101, 85760131222, 287369842623, 120773832179, 83209719751, 1684374218587, 6358345589299, 6305601215112, 5800992744105, 33960226045484, 56924554232879, 11856046381401

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 8 of A257833.

Cf. similar sequences for p^k: A039678 (k=2), A249275 (k=3), A353937 (k=4), A353938 (k=5), A353939 (k=6), A353940 (k=7), A353942 (k=9), A353943 (k=10).

Programs

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^8)^(p-1)==1, return(b)))

Python

from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353941(n): return 2**8+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**8,True)[1]) # Chai Wah Wu, May 17 2022

Extensions

a(7)-a(8) from Amiram Eldar, May 12 2022

More terms from Jinyuan Wang, May 17 2022