A084196 - OEIS

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

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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 *)