A353938 Smallest b > 1 such that b^(p-1) == 1 (mod p^5) for p = prime(n).

33, 242, 1068, 1353, 27216, 109193, 15541, 133140, 495081, 1115402, 2754849, 1353359, 649828, 3228564, 2359835, 4694824, 7044514, 28538377, 1111415, 77588426, 16178110, 2553319, 9571390, 158485540, 18664438, 146773512, 45639527, 448251412, 48834112, 141076650

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 5 of A257833.

Cf. similar sequences for p^k: A039678 (k=2), A249275 (k=3), A353937 (k=4), A353939 (k=6), A353940 (k=7), A353941 (k=8), A353942 (k=9), A353943 (k=10).

Programs

Mathematica

a[n_] := Module[{p = Prime[n], b = 2}, While[PowerMod[b, p - 1, p^5] != 1, b++]; b]; Array[a, 12] (* Amiram Eldar, May 12 2022 *)

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^5)^(p-1)==1, return(b)))

Python

from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353938(n): return 2**5+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**5,True)[1]) # Chai Wah Wu, May 17 2022