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A187754 Number of ways of writing the n-th 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 (list; graph; refs; listen; history; text; internal format)
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: A023821 A262332 A262240 * A075258 A321745 A212629

Adjacent sequences:  A187751 A187752 A187753 * A187755 A187756 A187757

KEYWORD

nonn

AUTHOR

Fabio Mercurio, Jan 03 2013

STATUS

approved

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Last modified April 9 07:30 EDT 2020. Contains 333344 sequences. (Running on oeis4.)