A227282 - OEIS

%I #13 Dec 19 2013 00:31:58

%S 47,179,199,409,619,829,881,1091,1453,3499,3709,3919,10529,10627,

%T 10837,10859,11069,11279,14423,20771,22697,30097,30307,31583,31793,

%U 32363,41669,75703,93281,95747,120661,120737,120871,120947,129287,140603,153319,153529

%N First primes of arithmetic progressions of 7 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 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 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 p = 179 then the AP-5 is {179, 389, 599, 809, 1019, 1229, 1439} with the difference 7# = 210.

%t 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 Select[Prime[Range[15000]],And@@PrimeQ[NestList[210+#&,#,6]]&] (* _Harvey P. Dale_, Nov 16 2013 *)

%o (PARI) is(p)=forstep(k=p,p+1260,210,if(!isprime(k),return(0)));1 \\ _Charles R Greathouse IV_, Dec 19 2013

%Y Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227283, A227284, A227285, A227286.

%K nonn

%O 1,1

%A _Sameen Ahmed Khan_, Jul 05 2013