A263239 - OEIS

A263239

Euler pseudoprimes to base 9: composite integers such that abs(9^((n - 1)/2)) == 1 mod n.

%I #17 Nov 17 2019 03:50:57

%S 4,28,91,121,286,532,671,703,949,1036,1105,1541,1729,1891,2465,2665,

%T 2701,2821,3281,3367,3751,4636,4961,5551,6364,6601,7381,8401,8911,

%U 10585,11011,11476,12403,14383,15203,15457,15841,16471,16531,18721,19345,19684,23521,24046,24661,24727

%N Euler pseudoprimes to base 9: composite integers such that abs(9^((n - 1)/2)) == 1 mod n.

%C Even numbers are permitted since 9 is an integer square. - _Charles R Greathouse IV_, Oct 12 2015

%H Amiram Eldar, <a href="/A263239/b263239.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..116 from Daniel Lignon)

%t eulerPseudo9Q[n_]:=(Mod[9^((n-1)/2)+1,n]==0 ||Mod[9^((n-1)/2)-1,n]==0) && Not[PrimeQ[n]];

%t Select[Range[2,200000],eulerPseudo9Q]

%o (PARI) is(n) = abs(centerlift(Mod(3, n)^(n-1)))==1 && !isprime(n) && n>1 \\ _Charles R Greathouse IV_, Oct 12 2015

%Y Cf. A020138 (pseudoprimes to base 9).

%Y Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), A262053 (base 6), A262054 (base 7), A262055 (base 8).

%K nonn

%O 1,1

%A _Daniel Lignon_, Oct 12 2015