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%I #12 Jun 07 2022 16:42:22
%S 5,7,23,389,409,1511,5309,3373,7351,37223,19867,18593,142811,14563,
%T 13933,763271,276637,174491,363989,383179,180907,687179,8066923,
%U 913589,458069,6358777,2507093,5650871,9182389,5256071,10237391,9955009,4091393,24374033
%N Smallest of the first four consecutive primes that comprise two sets of primes with difference 2*n.
%C An equivalent definition of this sequence: smallest prime which gives a cluster of primes with the spacing pattern 2*n; x; 2*n, x > 0.
%C A229021 gives the record values. - _Arkadiusz Wesolowski_, Sep 11 2013
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%e Difference two - primes: 5, 7, 11, 13.
%e Difference four - primes: 7, 11, 13, 17.
%e Difference six - primes: 23, 29, 31, 37.
%t lst = {}; Do[a = 3; While[True, b = NextPrime[a]; If[b - a == n && NextPrime[b, 2] - NextPrime[b] == n, AppendTo[lst, a]; Break[]]; a = b], {n, 2, 68, 2}]; lst
%t Table[SelectFirst[Partition[Prime[Range[16*10^5]],4,1],AllTrue[{#[[2]]-#[[1]],#[[4]]- #[[3]]}, EvenQ]&&#[[2]]-#[[1]]==#[[4]]-#[[3]]==2n&],{n,35}][[All,1]] (* _Harvey P. Dale_, Jun 07 2022 *)
%Y Cf. A000230, A133429, A133430, A229021, A229028, A229030, A229033, A229034.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Jun 14 2013
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