A076471 Number of pairs (p,q) of successive primes with p+q<=n.

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

Offset: 1

Author

Reinhard Zumkeller, Oct 14 2002

Keywords

• nonn

Examples

			Pairs (p,q) of successive primes with p+q<=27: {(2,3), (3,5), (5,7), (7,11), (11,13)}, hence a(27)=5.
		

Links

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

Crossrefs

Cf. A000720, A056172, A076472, A076473.

Programs

Maple

f:= proc(n) local p;
  if n <= 4 then return 0 fi;
  p:= prevprime(ceil(n/2));
  if p + nextprime(p) <= n then numtheory:-pi(p) else numtheory:-pi(p)-1 fi
end proc:
map(f, [$1..100]); # Robert Israel, Dec 08 2024

Mathematica

With[{t=Total/@Partition[Prime[Range[100]],2,1]},Table[Count[t,?(#<=n&)],{n,100}]] (* _Harvey P. Dale, Apr 16 2015 *)

Formula

A056172(n)-1 <= a(n) <= A056172(n).

a(n) = A076472(n) + A076473(n).