A076472 Number of pairs (p,q) of successive primes with p+q<=n and gcd(p+q,n)>1.

0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 3, 0, 4, 2, 3, 0, 4, 1, 4, 3, 4, 0, 6, 0, 5, 4, 5, 2, 6, 0, 6, 5, 7, 0, 7, 0, 7, 7, 7, 0, 7, 1, 8, 6, 8, 0, 8, 2, 8, 6, 8, 0, 10, 0, 9, 7, 9, 4, 9, 0, 10, 7, 11, 0, 10, 0, 10, 8, 10, 1, 11, 0, 12, 8, 11, 0, 12, 4, 12, 9, 12, 0, 14, 4, 13, 10, 13, 4, 13

Offset: 1

Author

Reinhard Zumkeller, Oct 14 2002

Keywords

• nonn
• look

Examples

			n=27: gcd(2+3,27)=1, gcd(3+5,27)=1, gcd(5+7,27)=3, gcd(7+11,27)=9, gcd(11+13,27)=3, hence a(27)=3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076471, A076473.

Programs

Maple

f:= proc(n) local t,p,q,s;
  p:= 2; t:= 0;
  do
    q:= p; p:= nextprime(p);
    s:= q+p;
    if s > n then return t fi;
    if igcd(s,n) > 1 then t:= t+1 fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 08 2024

Mathematica

Table[Count[Total/@Partition[Prime[Range[n]],2,1],?(#<=n&&GCD[#,n]>1&)],{n,100}] (* _Harvey P. Dale, May 06 2018 *)

Formula

a(n) = A076471(n) - A076473(n).

For n>6: a(n)=0 iff n is prime.