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Least number m such that 10^m == +- 1 mod (10n + 1).
2

%I #17 Oct 22 2023 17:14:28

%S 1,6,15,5,16,30,35,9,3,2,3,11,65,46,75,33,18,90,95,33,15,48,6,15,25,

%T 28,5,14,96,42,155,53,55,30,6,171,78,42,176,100,8,70,215,42,10,230,78,

%U 6,245,166,24,26,58,270,252,16,285,246,98,150,69,66,315,16,30

%N Least number m such that 10^m == +- 1 mod (10n + 1).

%H Alois P. Heinz, <a href="/A003566/b003566.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)

%t lnm[n_]:=Module[{m=1},While[!MemberQ[{1,10n},PowerMod[10,m,10n+1]],m++];m]; Array[lnm,60] (* _Harvey P. Dale_, Feb 12 2022 *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_