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%I #18 May 18 2022 07:55:37
%S 1025,59048,3626068,135967276,1509748675,14149342837,109522148350,
%T 649340249056,191730243526,45941644105613,6359301533362,
%U 24287026146320,265934493600922,927939012431924,1377672497815095,4440230734662684,10400007512898615,12198961352308417
%N Smallest b > 1 such that b^(p-1) == 1 (mod p^10) for p = prime(n).
%o (PARI) a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^10)^(p-1)==1, return(b)))
%o (Python)
%o from sympy.ntheory.residue_ntheory import nthroot_mod
%o from sympy import prime
%o 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
%Y Row k = 10 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), A353942 (k=9).
%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