A353943 Smallest b > 1 such that b^(p-1) == 1 (mod p^10) for p = prime(n).

1025, 59048, 3626068, 135967276, 1509748675, 14149342837, 109522148350, 649340249056, 191730243526, 45941644105613, 6359301533362, 24287026146320, 265934493600922, 927939012431924, 1377672497815095, 4440230734662684, 10400007512898615, 12198961352308417

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 10 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), A353942 (k=9).

Programs

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^10)^(p-1)==1, return(b)))

Python

from sympy.ntheory.residue_ntheory import nthroot_mod
from sympy import prime
def A353943(n): return 2**10+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**10,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