OFFSET
1,1
COMMENTS
Extension of k-Knödel numbers to k negative, in this case equal to -2. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+2) = 1 mod n.
All terms are even numbers.
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Knödel Numbers
MAPLE
with(numtheory); ListA225506:=proc(q, k) local a, n, ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a, n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225506(10^6, -2);
MATHEMATICA
Select[Range[10000], CompositeQ[#] && Divisible[# + 2, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
PROG
(PARI)
is(n) = forprime(p=3, n, if (n%p != 0 && Mod(p, n)^(n+2) != 1, return(0))); 1;
seq(N) = {
my(a=vector(N), k=0, n=4);
while(k < N, if(is(n), a[k++] = n); n += 2);
a;
};
seq(50) \\ Gheorghe Coserea, Dec 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 09 2013
EXTENSIONS
More terms from Gheorghe Coserea, Dec 23 2018
STATUS
approved