OFFSET
1,1
COMMENTS
All terms are odd composite numbers. There are no pseudoprimes to bases 2 or 3 in this sequence.
Are there infinitely many numbers of this kind?
From Max Alekseyev, Apr 16 2017: (Start)
Also, Fermat pseudoprimes base 2/3 that are not Fermat pseudoprimes base 2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
2^64 = 18446744073709551616 = 65 * 283796062672454640 + 16 and 3^64 = 3433683820292512484657849089281 = 65 * 52825904927577115148582293681 + 16. Therefore 65 is in the sequence.
Note: a(3) = 529 = 23^2 and a(40) = 47081 = 23^2 * 89.
MAPLE
filter:= proc(n) local t;
t:= 3 &^(n-1) mod n;
if t = 1 then return false fi;
t = 2 &^(n-1) mod n;
end proc:
select(filter, [seq(i, i=3..10^5, 2)]); # Robert Israel, Apr 27 2017
MATHEMATICA
Select[Range[2, 10^5], PowerMod[2, # - 1, #] == PowerMod[3, # - 1, #] != 1 &] (* Giovanni Resta, Apr 16 2017 *)
PROG
(PARI) is(n) = Mod(3, n)^(n-1)==2^(n-1) && Mod(2, n)^(n-1)!=1 \\ Felix Fröhlich, Apr 27 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Apr 16 2017
EXTENSIONS
More terms from Giovanni Resta, Apr 16 2017
STATUS
approved