A226039 Numbers k such that there exist primes p which divide k+1 and p-1 does not divide k.

5, 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 32, 33, 34, 35, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Peter Luschny, Generalized Bernoulli numbers.

Example

20 is in this list because 7 divides 21 but 6 does not divide 20.

Maple

s := (p, n) -> ((n+1) mod p = 0) and (n mod (p-1) <> 0);
F := n -> select(p -> s(p, n), select('isprime', [$2..n]));
A226039_list := n -> select(k -> [] <> F(k), [$0..n]);
A226039_list(103);

Mathematica

selQ[n_] := AnyTrue[Prime[Range[PrimePi[n+1]]], Divisible[n+1, #] && !Divisible[n, #-1]&];
Select[Range[103], selQ] (* Jean-François Alcover, Jul 08 2019 *)

Prog

(Sage)
def F(n): return any(p for p in primes(n) if (n+1) % p == 0 and n % (p-1) != 0)
def A226039_list(n): return list(filter(F, (0..n)))
A226039_list(103)

Crossrefs

Cf. A226038, A226040.

Sequence in context: A118358 A101731 A080765 * A257292 A234285 A314584

Adjacent sequences: A226036 A226037 A226038 * A226040 A226041 A226042

Keyword

nonn

Author

Peter Luschny, May 27 2013

Status

approved