cp's OEIS Frontend

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

%I A084196 #8 Aug 11 2023 13:15:44
%S A084196 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,
%T A084196 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,
%U A084196 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
%N A084196 Number of primes q<prime(n) such that q+1 divides prime(n)+1.
%C A084196 a(A049084(A082539(n)))=0, a(A049084(A084197(n)))>0, a(A049084(A084198(n)))=1;
%H A084196 Reinhard Zumkeller, <a href="/A084196/b084196.txt">Table of n, a(n) for n = 1..10000</a>
%e A084196 n=5, prime(5)=11: (11+1) mod (q+1) = 0 for 3 primes q<11: 2, 3,
%e A084196 and 5, therefore a(5)=3.
%t A084196 Table[Count[Mod[p+1,Prime[Range[PrimePi[p]-1]]+1],0],{p,Prime[Range[110]]}] (* _Harvey P. Dale_, Aug 11 2023 *)
%o A084196 (Haskell)
%o A084196 a084196 n = a084196_list !! (n-1)
%o A084196 a084196_list = f [] a000040_list where
%o A084196    f ps' (p:ps) = length [q | q <- ps', mod (p + 1) (q + 1) == 0] :
%o A084196                   f (p : ps') ps where
%o A084196 -- _Reinhard Zumkeller_, Jan 06 2014
%Y A084196 Cf. A084198, A084200.
%K A084196 nonn
%O A084196 1,5
%A A084196 _Reinhard Zumkeller_, May 18 2003