|
|
A260384
|
|
Maximal gap between successive elements of Pn with n >= 3. Pn : primes p <= A002110(n) such that q=2*A002110(n)-p is prime. (p, q) is a pair of centered primes at n-th primorial.
|
|
1
|
|
|
|
OFFSET
|
3,1
|
|
LINKS
|
|
|
EXAMPLE
|
For n=3, primorial(3)=A002110(3) is 30 and P3 is (7, 13, 17, 19, 23, 29) because (53, 47, 43, 41, 37, 31) are all prime. The maximum gap between two consecutive terms of P3 is 6, obtained for (7,13) or (23,29), so a(3)=6.
|
|
PROG
|
(PARI) lstp(n)=my(v = []); pn = prod(i=1, n, prime(i)); forprime(p=1, pn-1, if (isprime(2*pn-p), v = concat(v, p))); my(w = vector(#v-1, k, v[k+1] - v[k])); vecmax(w); \\ Michel Marcus, Jul 24 2015
(PARI) a(n)=my(P=2*prod(i=1, n, prime(i)), r, last=P); forprime(p=2, P/2, if(isprime(P-p), r=max(r, p-last); last=p)); r \\ Charles R Greathouse IV, Jul 24 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|