A076471 -id:A076471 - cp's OEIS frontend

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

Reinhard Zumkeller, Oct 14 2002

			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.

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

Cf. A076471, A076473.

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

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

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

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

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

Original entry on oeis.org

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

Reinhard Zumkeller, Oct 14 2002

			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.

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

Cf. A000010, A076471, A076472.

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

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

cp's OEIS Frontend

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

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