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Composite numbers with both 10 and -10 as primitive root.
1

%I #18 Nov 06 2012 16:15:09

%S 289,841,3721,4913,9409,11881,12769,22201,24389,32761,37249,52441,

%T 54289,66049,72361,83521,97969,113569,151321,187489,212521,226981,

%U 259081,292681,332929,351649,491401,502681,674041,707281,734449,877969,885481,908209,912673

%N Composite numbers with both 10 and -10 as primitive root.

%C The powers of primes from A007349.

%C Intersection of A002808, A167797 and A167806.

%H Arkadiusz Wesolowski, <a href="/A218766/b218766.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitiveRoot.html">Primitive Root</a>

%e 12769 = 113^2 belongs to this sequence because 113 is in A007349.

%t lst = {}; r = 912673; Do[If[PrimeQ[i] && MultiplicativeOrder[10, i] == MultiplicativeOrder[-10, i] == i - 1, n = 2; While[(p = i^n) <= r, AppendTo[lst, p]; n++]], {i, Floor@Sqrt[r]}]; Sort[lst]

%Y Cf. A007349.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Nov 05 2012