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
Keywords
Examples
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).
Programs
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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
Extensions
Corrected and extended by Rick L. Shepherd, Sep 08 2003
Comments