A353942 Smallest b > 1 such that b^(p-1) == 1 (mod p^9) for p = prime(n).

513, 19682, 280182, 14906455, 676386984, 822557039, 8185328614, 1835323405, 147534349327, 430099398783, 746688111476, 3054750102760, 9430469115218, 42562034654367, 92084372092298, 28307243117603, 17362132628379, 430275700643181, 478910674129864, 69114209866295

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 9 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), A353941 (k=8), A353943 (k=10).

Programs

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^9)^(p-1)==1, return(b)))

Python

from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353942(n): return 2**9+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**9,True)[1]) # Chai Wah Wu, May 17 2022

Extensions

a(5)-a(6) from Amiram Eldar, May 12 2022

More terms from Jinyuan Wang, May 17 2022