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A190838 Initial primes of 8 consecutive primes with 7 consecutive gaps 2, 4, 6, 8, 10, 12, 14.

%I A190838 #33 May 01 2024 13:14:49
%S A190838 128981,21456047,34864211,51867197,55793951,69726647,113575727,
%T A190838 180078317,207664397,232728647,342241967,382427027,382533311,
%U A190838 470463011,558791327,591360851,603413801,749930717,838115711,926976431,965761397,1007421251,1109867567,1278189947
%N A190838 Initial primes of 8 consecutive primes with 7 consecutive gaps 2, 4, 6, 8, 10, 12, 14.
%C A190838 a(1) = 128981 = A190819(1), a(2) = 21456047 = A190819(14).
%C A190838 a(n) + 56 is the greatest term in the sequence of 8 consecutive primes with 7 consecutive gaps 2, 4, 6, 8, 10, 12, 14. - _Muniru A Asiru_, Aug 10 2017
%H A190838 Charles R Greathouse IV, <a href="/A190838/b190838.txt">Table of n, a(n) for n = 1..10000</a>
%H A190838 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%p A190838 N:=10^8:  # to get all terms <= N.
%p A190838 Primes:=select(isprime,[seq(i,i=3..N+56,2)]):
%p A190838 Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],
%p A190838   Primes[t+3]-Primes[t+2], Primes[t+4]-Primes[t+3], Primes[t+5]-
%p A190838   Primes[t+4], Primes[t+6]-Primes[t+5] , Primes[t+7]-Primes[t+6] ]=
%p A190838 [2,4,6,8,10,12,14], [$1..nops(Primes)-7])]; # _Muniru A Asiru_, Aug 04 2017
%t A190838 Transpose[Select[Partition[Prime[Range[65000000]],8,1],Differences[#] =={2,4,6,8,10,12,14}&]][[1]] (* _Harvey P. Dale_, May 10 2014 *)
%o A190838 (PARI) list(lim)=my(v=List(),p=128981,t); forprime(q=p+2,lim+56, if(q-p-t==2, t+=2; if(t==14, listput(v, q-56); t=0), t=0); p=q); Vec(v) \\ _Charles R Greathouse IV_, Aug 10 2017
%Y A190838 Subsequence of A190819.
%Y A190838 Subsequence of A187060. - _Michel Marcus_, Aug 10 2017
%Y A190838 Cf. A078847, A190814, A190817.
%K A190838 nonn
%O A190838 1,1
%A A190838 _Zak Seidov_, May 21 2011
%E A190838 Additional cross references from _Harvey P. Dale_, May 10 2014