A079023 Let p and q be two prime numbers, not necessarily consecutive, such that q - p = 2n; then a(n) is the number of partitions of 2n into even numbers so that each partition corresponds to a consecutive prime difference pattern (k-tuple) and p <= A000230(n).

1, 2, 6, 9, 14, 24, 11, 56, 46, 45, 46, 109, 82, 97, 287, 124, 51, 390, 507, 434, 691, 332, 1105, 898, 676, 359, 1080, 1259, 659, 1688, 540, 1146, 4081, 1672, 3081, 985, 3975, 2423, 4460, 6512, 2779, 10324, 1820, 5458, 10273, 8196, 9177, 7085, 6462, 5037

Offset

1,2

Comments

Partitions are counted with multiplicity and may overlap.

Links

Table of n, a(n) for n=1..50.

Example

Only those partitions are counted that appear not later than prime A000230(n); n=7, d=14, A000230(7)=113; the number of solutions to p+14=q, with p and q both prime and p <= 113, is 11. These 11 (not necessarily distinct) partitions and their initial primes are as follows: 3[22424], 5[24242], 17[2462], 23[626], 29[2642], 47[662], 53[626], 59[2642], 83[68], 89[842], 113[14]=A000230(7).

Prog

(PARI) {for(n=1, 50, c=0; p=2; done=0; until(done, if(isprime(p+2*n), c++; if(nextprime(p+1)-p==2*n, done=1; print1(c, ", "))); p=nextprime(p+1)))} \\ Rick L. Shepherd

Crossrefs

Cf. A000230, A079015-A079024.

Sequence in context: A342426 A217001 A320666 * A327967 A189760 A363373

Adjacent sequences: A079020 A079021 A079022 * A079024 A079025 A079026

Keyword

nonn

Author

Labos Elemer, Jan 24 2003

Extensions

Corrected and extended by Rick L. Shepherd, Sep 08 2003

Status

approved