A187754 Number of ways of writing the n-th twin prime p as p = q + r + s, where q >= r >= s are twin primes.

0, 0, 0, 1, 2, 3, 3, 6, 5, 8, 7, 7, 8, 8, 9, 10, 12, 14, 13, 15, 14, 21, 20, 20, 22, 22, 23, 23, 24, 36, 34, 36, 38, 42, 44, 43, 44, 51, 53, 59, 56, 48, 53, 57, 58, 57, 60, 75, 78, 87, 87, 78, 79, 67, 65

Offset

1,5

Comments

The author conjectures that a(n) >= 1 for all n >= 4.

By Zhi-Wei Sun's conjecture related to A219157, for any positive integer n not among 1, 10, 430 we can write 6n-1 = p+2q = p+q+q with p,p-2,q,q+2 all prime, also for any integer n>702 we can write 6n+1 = 6(n-1)+7 = p+q+7 with p,p-2,q,q+2 all prime. Thus the author's conjecture is a consequence of Sun's conjecture. - Zhi-Wei Sun, Jan 06 2013

Links

Table of n, a(n) for n=1..55.

Example

a(9) = 5 because the ninth twin prime, A001097(9), is 31, and 31 can be written as a sum of three twin primes in 5 distinct ways: 3+11+17, 5+7+19, 5+13+13, 7+7+17, and 7+11+13.

Prog

(PARI) isA001097(n) = (isprime(n) & (isprime(n+2) || isprime(n-2)))
A187754(n) = {local(q, r, s, a); a=0; for( q=1, n, if( isA001097(q), for( r=1, q, if( isA001097(r), for( s=1, r, if( isA001097(s) && (n==q+r+s), a=a+1)))))); a}
n=1; for( p=1, 700, if( isA001097(p), print(n, " ", A187754(p)); n=n+1)) /* Michael B. Porter, Jan 05 2013 */

Crossrefs

Cf. A001097.

Sequence in context: A262332 A262240 A333660 * A347732 A075258 A321745

Adjacent sequences: A187751 A187752 A187753 * A187755 A187756 A187757

Keyword

nonn

Author

Fabio Mercurio, Jan 03 2013

Status

approved