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%I #16 May 18 2022 07:55:34
%S 513,19682,280182,14906455,676386984,822557039,8185328614,1835323405,
%T 147534349327,430099398783,746688111476,3054750102760,9430469115218,
%U 42562034654367,92084372092298,28307243117603,17362132628379,430275700643181,478910674129864,69114209866295
%N Smallest b > 1 such that b^(p-1) == 1 (mod p^9) for p = prime(n).
%o (PARI) a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^9)^(p-1)==1, return(b)))
%o (Python)
%o from sympy import prime
%o from sympy.ntheory.residue_ntheory import nthroot_mod
%o 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
%Y Row k = 9 of A257833.
%Y 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).
%K nonn
%O 1,1
%A _Felix Fröhlich_, May 12 2022
%E a(5)-a(6) from _Amiram Eldar_, May 12 2022
%E More terms from _Jinyuan Wang_, May 17 2022
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