A190817 - OEIS

%I #51 Sep 03 2017 21:55:59

%S 13901,21557,28277,55661,68897,128981,221717,354371,548831,665111,

%T 954257,1164587,1246367,1265081,1538081,1595051,1634441,2200811,

%U 2798921,2858621,3053747,3407081,3414011,3967487,3992201,4480241,4608281,4701731,4809251,5029457

%N Initial primes of 6 consecutive primes with consecutive gaps 2,4,6,8,10.

%C a(1) = 13901 = A190814(5) = A187058(7) = A078847(24).

%C a(n) + 30 is the greatest term in the sequence of 6 consecutive primes with consecutive gaps 2, 4, 6, 8, 10. - _Muniru A Asiru_, Aug 10 2017

%H Zak Seidov, <a href="/A190817/b190817.txt">Table of n, a(n) for n = 1..6000</a>

%H R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>

%e For n = 1, 13901 is in the sequence because 13901, 13903, 13907, 13913, 13921, 13931 are consecutive primes and for n = 2, 21557 is in the sequence since 21557, 21559, 21563, 21569, 21577, 21587 are consecutive primes. - _Muniru A Asiru_, Aug 24 2017

%p N:=10^7: # to get all terms <= N.

%p Primes:=select(isprime,[seq(i,i=3..N+30,2)]):

%p 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]]=[2,4,6,8,10], [$1..nops(Primes)-5])]; # _Muniru A Asiru_, Aug 04 2017

%t d = Differences[Prime[Range[100000]]]; Prime[Flatten[Position[Partition[d, 5, 1], {2, 4, 6, 8, 10}]]] (* _T. D. Noe_, May 23 2011 *)

%t With[{s = Differences@ Prime@ Range[10^6]}, Prime[SequencePosition[s, Range[2, 10, 2]][[All, 1]] ] ] (* _Michael De Vlieger_, Aug 16 2017 *)

%o (PARI) lista(nn) = forprime(p=13901, nn, if(nextprime(p+1)==p+2 && nextprime(p+3)==p+6 && nextprime(p+7)==p+12 && nextprime(p+13)==p+20 && nextprime(p+21)==p+30, print1(p", "))); \\ _Altug Alkan_, Aug 16 2017

%o (GAP)

%o K:=3*10^7+1;; # to get all terms <= K.

%o P:=Filtered([1,3..K],IsPrime);; I:=[2,4,6,8,10];;

%o P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;

%o P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4]]);;

%o P3:=List(Positions(P2,I),i->P[i]);  # _Muniru A Asiru_, Aug 24 2017

%Y Cf. A078847, A187058, A190814, A190819, A190838.

%K nonn

%O 1,1

%A _Zak Seidov_, May 21 2011

%E Additional cross references from _Harvey P. Dale_, May 10 2014