A263239 Euler pseudoprimes to base 9: composite integers such that abs(9^((n - 1)/2)) == 1 mod n.

4, 28, 91, 121, 286, 532, 671, 703, 949, 1036, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4636, 4961, 5551, 6364, 6601, 7381, 8401, 8911, 10585, 11011, 11476, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345, 19684, 23521, 24046, 24661, 24727

Offset

1,1

Comments

Even numbers are permitted since 9 is an integer square. - Charles R Greathouse IV, Oct 12 2015

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..116 from Daniel Lignon)

Mathematica

eulerPseudo9Q[n_]:=(Mod[9^((n-1)/2)+1, n]==0 ||Mod[9^((n-1)/2)-1, n]==0) && Not[PrimeQ[n]];
Select[Range[2, 200000], eulerPseudo9Q]

Prog

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

Crossrefs

Cf. A020138 (pseudoprimes to base 9).

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

Sequence in context: A183485 A183437 A294315 * A296015 A187452 A173296

Adjacent sequences: A263236 A263237 A263238 * A263240 A263241 A263242

Keyword

nonn

Author

Daniel Lignon, Oct 12 2015

Status

approved