

A187754


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


1



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
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OFFSET

1,5


COMMENTS

The author conjectures that a(n) >= 1 for all n >= 4.
By ZhiWei Sun's conjecture related to A219157, for any positive integer n not among 1, 10, 430 we can write 6n1 = p+2q = p+q+q with p,p2,q,q+2 all prime, also for any integer n>702 we can write 6n+1 = 6(n1)+7 = p+q+7 with p,p2,q,q+2 all prime. Thus the author's conjecture is a consequence of Sun's conjecture.  ZhiWei 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(n2)))
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: A023821 A262332 A262240 * A075258 A321745 A212629
Adjacent sequences: A187751 A187752 A187753 * A187755 A187756 A187757


KEYWORD

nonn


AUTHOR

Fabio Mercurio, Jan 03 2013


STATUS

approved



