A270992 Number of distinct prime divisors of prime(n)+1 and prime(n+1)+1.

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1

Offset: 1

Author

Michel Marcus, Mar 28 2016

Keywords

• nonn

Examples

			For n=1, p=2 and q=3; 3 and 4 have no common prime divisor, so a(1)=0.
For n=2, p=3 and q=5; 4 and 6 have 1 common prime divisor, so a(2)=1.
For n=9, p=23 and q=29; 24 and 30 have 2 common prime divisors, so a(9)=2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008335, A270592 (records).

Programs

Mathematica

Table[Length[Map[First, FactorInteger[GCD @@ {Prime@ n + 1, Prime[n + 1] + 1}]] /. 1 -> Nothing], {n, 101}] (* Michael De Vlieger, Mar 28 2016 *)
Length[Intersection[FactorInteger[#[[1]]+1][[All,1]],FactorInteger[#[[2]] + 1][[All,1]]]]&/@Partition[Prime[Range[120]],2,1] (* Harvey P. Dale, Jun 11 2017 *)

PARI

lista(nn) = {p = 2; f = factor(p+1)[,1]~; forprime(q=3, nn, g = factor(q+1)[,1]~; print1(#setintersect(f, g), ", "); p = q; f = g;);}

PARI

a(n) = my(p = prime(n), q = nextprime(p+1)); #setintersect(factor(p+1)[,1]~, factor(q+1)[,1]~);