A084196 Number of primes q<prime(n) such that q+1 divides prime(n)+1.

0, 0, 1, 1, 3, 0, 2, 1, 5, 2, 2, 0, 3, 1, 6, 3, 6, 0, 1, 7, 0, 3, 6, 4, 1, 2, 2, 6, 0, 3, 3, 5, 2, 3, 3, 3, 0, 1, 9, 2, 9, 1, 8, 0, 3, 3, 1, 4, 6, 0, 3, 11, 0, 8, 2, 8, 6, 3, 0, 2, 1, 5, 3, 7, 0, 2, 1, 0, 5, 1, 2, 13, 2, 0, 3, 10, 3, 0, 2, 0, 11, 0, 11, 2, 5, 5, 6, 0, 4, 2, 6, 13, 2, 5, 2, 13, 4, 4, 1, 0, 1, 4

Offset

1,5

Comments

a(A049084(A082539(n)))=0, a(A049084(A084197(n)))>0, a(A049084(A084198(n)))=1;

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=5, prime(5)=11: (11+1) mod (q+1) = 0 for 3 primes q<11: 2, 3,
and 5, therefore a(5)=3.

Mathematica

Table[Count[Mod[p+1, Prime[Range[PrimePi[p]-1]]+1], 0], {p, Prime[Range[110]]}] (* Harvey P. Dale, Aug 11 2023 *)

Prog

(Haskell)
a084196 n = a084196_list !! (n-1)
a084196_list = f [] a000040_list where
   f ps' (p:ps) = length [q | q <- ps', mod (p + 1) (q + 1) == 0] :
                  f (p : ps') ps where
-- Reinhard Zumkeller, Jan 06 2014

Crossrefs

Cf. A084198, A084200.

Sequence in context: A268464 A165066 A034389 * A295041 A359710 A127913

Adjacent sequences: A084193 A084194 A084195 * A084197 A084198 A084199

Keyword

nonn

Author

Reinhard Zumkeller, May 18 2003

Status

approved