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

1,10

Links

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

Formula

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

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

Example

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.

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 *)

Crossrefs

Cf. A076471, A076473.

Sequence in context: A276812 A246721 A249441 * A161840 A355851 A140302

Adjacent sequences: A076469 A076470 A076471 * A076473 A076474 A076475

Keyword

nonn,look

Author

Reinhard Zumkeller, Oct 14 2002

Status

approved