A353940 Smallest b > 1 such that b^(p-1) == 1 (mod p^7) for p = prime(n).

129, 2186, 32318, 82681, 758546, 6826318, 21444846, 44702922, 178042767, 393747520, 1548729003, 4741156070, 2203471139, 3242334565, 16609835418, 114175761515, 30338830655, 20115543070, 114457309347, 370162324382, 57877856575, 12692933349, 280646695286, 127762186531

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 7 of A257833.

Cf. similar sequences for p^k: A039678 (k=2), A249275 (k=3), A353937 (k=4), A353938 (k=5), A353939 (k=6), A353941 (k=8), A353942 (k=9), A353943 (k=10).

Programs

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^7)^(p-1)==1, return(b)))

Python

from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353940(n): return 2**7+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**7,True)[1]) # Chai Wah Wu, May 17 2022

Extensions

a(9)-a(11) from Amiram Eldar, May 12 2022

More terms from Jinyuan Wang, May 17 2022