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A262051 Euler pseudoprimes to base 3: composite integers such that abs(3^((n - 1)/2)) == 1 mod n. 6

%I

%S 121,703,1541,1729,1891,2465,2821,3281,4961,7381,8401,8911,10585,

%T 12403,15457,15841,16531,18721,19345,23521,24661,28009,29341,30857,

%U 31621,31697,41041,44287,46657,47197,49141,50881,52633,55969,63139,63973,72041,74593,75361

%N Euler pseudoprimes to base 3: composite integers such that abs(3^((n - 1)/2)) == 1 mod n.

%H Amiram Eldar, <a href="/A262051/b262051.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..64 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[26000] + 1, eulerPseudoQ[#, 3] &] (* _Michael De Vlieger_, Sep 09 2015, after _Jean-Fran├žois Alcover_ at A006970 *)

%o (PARI) for(n=1, 1e5, if( Mod(3, (2*n+1))^n == 1 || Mod(3, (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), this sequence (base 3), A001567 (base 4), A262052 (base 5), A262053 (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 November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)