OFFSET
1,1
COMMENTS
The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
When a(n+1) = a(n) + 210, as for n = 1, 25, ..., then a(n) is in A094220: start of AP of 10 primes with common distance 210. - M. F. Hasler, Jan 02 2020
LINKS
Sameen Ahmed Khan, Table of n, a(n) for n = 1..47
OEIS wiki, Primes in arithmetic progression.
EXAMPLE
p = 409 then the AP-9 is {409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089} with the difference 9# = 2*3*5*7 = 210.
MATHEMATICA
Clear[p]; d = 210; ap9p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[ap9p, p]], {p, 3, 10^9, 2}]; ap9p
PROG
(PARI) v=[1..8]*210; forprime(p=1, , for(i=1, #v, isprime(p+v[i])||next(2)); print1(p", ")) \\ M. F. Hasler, Jan 02 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Sameen Ahmed Khan, Jul 05 2013
STATUS
approved