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

Comments

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

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

Links

Table of n, a(n) for n=1..96.

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.

Mathematica

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

Crossrefs

Sequence in context: A276812 A246721 A249441 * A161840 A355851 A140302

Adjacent sequences: A076469 A076470 A076471 * A076473 A076474 A076475

Keyword

nonn

Author

Reinhard Zumkeller, Oct 14 2002

Status

approved