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%I #28 Mar 29 2023 12:48:42
%S 6,12,14,24,28,34,46,48,52,56,68,72,84,92,96,112,117,123,126,136,144,
%T 168,186,192,204,208,224,228,249,252,266,272,288,328,336,356,372,384,
%U 392,408,416,448,464,488,498,504,516
%N Numbers n for which 10^n mod n = 2^k for some positive integer k.
%C Odd numbers in this sequence: 117, 123, 249, 747, 4043, 5031, 11573, 12129, 14481, 29489, 34719, 35549, 84123, 124631, 173329, 217391, 266799, 458523, 472173, 490561, 551759, 658499, 675431, 721773, 800397, 1375569, 1917843, 2300079, 3194787, 3394893, 4236747, 5031039, 5043957, 5169333, ....
%H Charles R Greathouse IV, <a href="/A293907/b293907.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 6, 10^6 mod 6 = 4 = 2^2;
%e For n = 14, 10^14 mod 14 = 2 = 2^1;
%e For n = 84, 10^84 mod 84 = 64 = 2^6;
%e For n = 272, 10^272 mod 272 = 256 = 2^8.
%t pm2Q[n_]:=Module[{c=PowerMod[10,n,n]},c>1&&IntegerQ[Log2[c]]]; Select[ Range[600],pm2Q] (* _Harvey P. Dale_, Mar 29 2023 *)
%o (PARI) is(n)=my(k=lift(Mod(10,n)^n)); k>1 && k>>valuation(k,2)==1 \\ _Charles R Greathouse IV_, Oct 19 2017
%Y Cf. A056969 (10^n modulo n).
%K nonn
%O 1,1
%A _Björn Ch. Buchli_, Oct 19 2017
%E More terms from _Michel Marcus_, Oct 19 2017
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