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A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.

%I A227282 #13 Dec 19 2013 00:31:58
%S A227282 47,179,199,409,619,829,881,1091,1453,3499,3709,3919,10529,10627,
%T A227282 10837,10859,11069,11279,14423,20771,22697,30097,30307,31583,31793,
%U A227282 32363,41669,75703,93281,95747,120661,120737,120871,120947,129287,140603,153319,153529
%N A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.
%C A227282 The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
%C A227282 For k = 7, we have d = 5*5# = 150 and there is ONLY one AP-7 with this difference: {7, 157, 307, 457, 607, 757, 907}.
%H A227282 Sameen Ahmed Khan and Charles R Greathouse IV, <a href="/A227282/b227282.txt">Table of n, a(n) for n = 1..10000</a> (first 2484 terms from Khan)
%e A227282 p = 179 then the AP-5 is {179, 389, 599, 809, 1019, 1229, 1439} with the difference 7# = 210.
%t A227282 Clear[p]; d = 210; ap7p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d}] == {True, True, True, True, True, True, True}, AppendTo[ap7p, p]], {p, 3, 10^9, 2}]; ap7p
%t A227282 Select[Prime[Range[15000]],And@@PrimeQ[NestList[210+#&,#,6]]&] (* _Harvey P. Dale_, Nov 16 2013 *)
%o A227282 (PARI) is(p)=forstep(k=p,p+1260,210,if(!isprime(k),return(0)));1 \\ _Charles R Greathouse IV_, Dec 19 2013
%Y A227282 Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227283, A227284, A227285, A227286.
%K A227282 nonn
%O A227282 1,1
%A A227282 _Sameen Ahmed Khan_, Jul 05 2013