%I #13 Jan 03 2020 05:31:53
%S 199,409,3499,10859,564973,1288607,1302281,2358841,3600521,4047803,
%T 17160749,20751193,23241473,44687567,50655739,53235151,87662609,
%U 100174043,103468003,110094161,180885839,187874017,192205147,221712811,243051733,243051943,304570103
%N First primes of arithmetic progressions of 9 primes each with the common difference 210.
%C The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
%C 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
%H Sameen Ahmed Khan, <a href="/A227284/b227284.txt">Table of n, a(n) for n = 1..47</a>
%H OEIS wiki, <a href="https://oeis.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%e 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.
%t 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
%o (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
%Y Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227285, A227286.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Jul 05 2013