A076473 Number of pairs (p,q) of successive primes with p+q<=n and gcd(p+q,n)=1.

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

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)=2.
		

Links

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

Crossrefs

Cf. A000010, A076471, A076472.

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

Formula

a(n) = A076471(n) - A076472(n).