A190819 - OEIS

%I #30 Feb 18 2022 13:43:55

%S 128981,665111,2798921,3992201,5071667,5093507,5344247,10732817,

%T 11920367,16197947,16462541,16655447,16943471,21456047,25793897,

%U 32634311,34051007,34864211,35250431,38585201,39898757,49584371,50375861,51867197,54738767,55793951

%N Initial primes of 7 consecutive primes with consecutive gaps 2, 4, 6, 8, 10, 12.

%C Subsequence of A190817, a(1) = 128981 = A190817(6).

%C a(n) + 42 is the greatest term in the sequence of 7 consecutive primes with 6 consecutive gaps 2, 4, 6, 8, 10, 12. - _Muniru A Asiru_, Aug 10 2017

%H Zak Seidov, <a href="/A190819/b190819.txt">Table of n, a(n) for n = 1..300</a>

%e Prime(12073..12079) = {128981, 128983, 128987, 128993, 129001, 129011, 129023} with first differences {2, 4, 6, 8, 10, 12}.

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

%p Primes:=select(isprime,[seq(i,i=3..N+42,2)]):

%p Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],

%p Primes[t+3]-Primes[t+2], Primes[t+4]-Primes[t+3], Primes[t+5]-Primes[t+4], Primes[t+6]-Primes[t+5] ]=[2,4,6,8,10,12], [$1..nops(Primes)-6])]; # _Muniru A Asiru_, Aug 04 2017

%t d = Differences[Prime[Range[1000000]]]; Prime[Flatten[Position[Partition[d, 6, 1], {2, 4, 6, 8, 10, 12}]]] (* _T. D. Noe_, May 23 2011 *)

%t Prime[SequencePosition[Differences[Prime[Range[34*10^5]]],{2,4,6,8,10,12}][[All,1]]] (* _Harvey P. Dale_, Feb 18 2022 *)

%Y Cf. A078847, A190814, A190817, A190838.

%K nonn

%O 1,1

%A _Zak Seidov_, May 21 2011

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