A225506 -2-Knödel numbers.

4, 6, 8, 10, 12, 24, 28, 30, 70, 88, 130, 238, 510, 754, 868, 910, 1330, 2068, 2590, 2728, 3304, 4002, 5110, 5406, 8554, 8710, 12958, 15748, 18430, 20878, 21238, 23902, 24178, 32422, 39928, 46870, 49210, 53590, 55678, 57358, 62248, 67858, 70414, 79378, 88198, 95038, 95758, 95788, 102238, 114478

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

Cf. A208728.

Cf. A225507, A225508, A225509, A225510, A225511, A225512, A225513, A225514.

Sequence in context: A359202 A096160 A181055 * A073669 A073670 A090169

Adjacent sequences: A225503 A225504 A225505 * A225507 A225508 A225509

Keyword

nonn

Author

Paolo P. Lava, May 09 2013

Extensions

More terms from Gheorghe Coserea, Dec 23 2018

Status

approved