A139602
The smallest prime p that makes the pair p+/-6n both primes while no other pair of p+/-6k+6*n, 0
11, 19, 61, 43, 97, 163, 191, 229, 283, 223, 743, 991, 541, 457, 877, 1327, 1049, 1321, 1733, 1307, 1987, 6011, 2971, 5153, 2029, 8693, 2551, 4789, 5407, 2129, 6473, 4481, 4889, 4217, 7951, 11743, 13789, 9851, 7253, 11491, 20393, 17231, 9749, 20747, 6599, 13873, 16369, 15461, 17123, 13451, 9967, 26959, 21089, 41863, 27437, 26003, 40189, 18661, 16673, 64693
Offset: 1
Keywords
Examples
For n = 1, 11-6n=5, 11+6n=17, are both primes, and for any prime number p smaller than 11, it is impossible that p-6 is prime; For n = 2, 19-6n=7, 19+6n=31, are both primes,while 19+6*1=25 is not prime. For primes p<19, either p+/-6 are prime pairs, or p+/-12 are not a prime pair; ... for n = 6, 163-6n=127, 163+6n=199, are both primes,while 163+6*k, k=1,2,4 and 163-6*k, k=3,5 are not primes. For primes p<163, either exists prime pair p+/-6k, 0<k<6, or p+/-36 are not a prime pair.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
BothPrime[p_, k_] := PrimeQ[p + 6*k] && PrimeQ[p - 6*k]; f[n_] := Module[{p,k}, p = Prime[PrimePi[6*n] + 1]; While[k = 1; While[k < n && ! BothPrime[p, k], k++]; k < n || ! BothPrime[p, n], p = NextPrime[p]]; p]; Table[f[n], {n,60}] -
PARI
a(n)=forprime(p=2,default(primelimit),if(!isprime(p-6*n) || !isprime(p+6*n), next); for(k=1,n-1,if(isprime(p-6*k) && isprime(p+6*k), next(2))); return(p)) \\ Charles R Greathouse IV, Mar 22 2011
Comments