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A286891 Initial primes of 6 consecutive primes with 5 consecutive gaps 10, 8, 6, 4, 2.

%I A286891 #29 Jul 20 2025 06:59:17
%S A286891 41203,556243,576193,715849,752263,859249,891799,1107763,1191079,
%T A286891 1201999,1210369,1510189,1601599,1893163,2530963,2678719,2881243,
%U A286891 3257689,3431479,3545263,3792949,3804919,4041109,4479463,4867309
%N A286891 Initial primes of 6 consecutive primes with 5 consecutive gaps 10, 8, 6, 4, 2.
%C A286891 All terms = {13,19} mod 30.
%C A286891 For initial primes of 6 consecutive primes with consecutive gaps 2, 4, 6, 8, 10 see A190817.
%H A286891 Chai Wah Wu, <a href="/A286891/b286891.txt">Table of n, a(n) for n = 1..10000</a>
%H A286891 R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>
%e A286891 Prime(4313..4318) = {41203, 41213, 41221, 41227, 41231, 41233} and 41203 + 10 = 41213, 41213 + 8 = 41221, 41221 + 6 = 41227, 41227 + 4 = 41231, 41231 + 2 = 41233.
%e A286891 Also, prime(68287..68292) = {859249, 859259, 859267, 859273, 859277, 859279} and 859249 + 10 = 859259, 859259 + 8 = 859267, 859267 + 6 = 859273, 859273 + 4 = 859277, 859277 + 2 = 859279.
%p A286891 K:=10^7: # to get all terms <= K.
%p A286891 Primes:=select(isprime,[seq(i,i=3..K+30,2)]): Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1], Primes[t+3]-Primes[t+2], Primes[t+4]-Primes[t+3], Primes[t+5]-Primes[t+4]]=[10,8,6,4,2], [$1..nops(Primes)-5])]; # _Muniru A Asiru_, Aug 15 2017
%t A286891 Select[Partition[Prime[Range[340000]],6,1],Differences[#]=={10,8,6,4,2}&][[All,1]] (* _Harvey P. Dale_, Aug 22 2018 *)
%o A286891 (GAP)
%o A286891 P:=Filtered([1..20000000],IsPrime);;  I:=Reversed([2,4,6,8,10]);;
%o A286891 P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
%o A286891 P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4]]);;
%o A286891 P3:=List(Positions(P2,I),i->P[i]);
%Y A286891 Cf. A078847, A190814, A190817, A190819, A190838, A290161, A290162.
%Y A286891 Subsequence of A031928.
%K A286891 nonn
%O A286891 1,1
%A A286891 _Muniru A Asiru_, Jul 22 2017