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 A262053 Euler pseudoprimes to base 6: composite integers such that abs(6^((n - 1)/2)) == 1 mod n. 6

%I

%S 185,217,301,481,1111,1261,1333,1729,2465,2701,3421,3565,3589,3913,

%T 5713,6533,8365,10585,11041,11137,12209,14701,15841,17329,18361,20017,

%U 21049,22049,29341,31021,31621,34441,36301,38081,39305,39493,41041,43621,44801,46657

%N Euler pseudoprimes to base 6: composite integers such that abs(6^((n - 1)/2)) == 1 mod n.

%H Amiram Eldar, <a href="/A262053/b262053.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..86 from Daniel Lignon)

%t eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[25000] + 1, eulerPseudoQ[#, 6] &] (* _Michael De Vlieger_, Sep 09 2015, after _Jean-François Alcover_ at A006970 *)

%o (PARI) for(n=1, 1e5, if( Mod(6, (2*n+1))^n == 1 || Mod(6, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ _Altug Alkan_, Oct 11 2015

%Y Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), this sequence (base 6), A262054 (base 7), A262055 (base 8).

%K nonn

%O 1,1

%A _Daniel Lignon_, Sep 09 2015

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Last modified December 7 03:27 EST 2019. Contains 329836 sequences. (Running on oeis4.)