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A284101 Initial primes of 14 consecutive primes all congruent to 5 mod 6.

%I A284101 #16 Sep 22 2024 19:00:18
%S A284101 19725473,19725479,40727657,40962983,40962989,44291297,45404537,
%T A284101 45404543,54470123,54470147,63846089,63846119,68208599,68208611,
%U A284101 68364221,90007661,93602507,99492971,99492977,99579647,99579671,117585977,117585983
%N A284101 Initial primes of 14 consecutive primes all congruent to 5 mod 6.
%C A284101 Prime indices of a(n): 1254203,1254204,2475221,2488622,2488623,2677942,2741244,2741245.
%C A284101 a(1) = 19725473 = A057622(14). Actually 19725473, 40962983 and 45404537 are the initial primes of 15 such consecutive primes that is also a(1) = A057622(15).
%H A284101 Charles R Greathouse IV, <a href="/A284101/b284101.txt">Table of n, a(n) for n = 1..10000</a>
%e A284101 15 consecutive primes starting with 19725473 are
%e A284101 {19725473, 19725479, 19725527, 19725533, 19725599, 19725617, 19725623, 19725653, 19725659, 19725677, 19725683, 19725689, 19725701, 19725731, 19725737} with gaps
%e A284101 {6, 48, 6, 66, 18, 6, 30, 6, 18, 6, 6, 12, 30, 6} - all multiples of 6.
%t A284101 Select[Partition[Prime[Range[68*10^5]],14,1],AllTrue[Mod[#,6]==5&]][[;;,1]] (* _Harvey P. Dale_, Mar 06 2023 *)
%t A284101 Prime[#]&/@(SequencePosition[If[Mod[#,6]==5,1,0]&/@Prime[Range[672*10^4]],PadRight[{},14,1]][[;;,1]]) (* _Harvey P. Dale_, Sep 22 2024 *)
%o A284101 (PARI) list(lim)=my(v=List(), P=primes(14), goal=vector(14,i,5), pm=P%6, idx=1); forprime(p=P[#P]+1,, P[idx]=p; pm[idx]=p%6; if(idx++>14,idx=1); if(P[idx]>lim, break); if(pm==goal, listput(v, P[idx]))); Vec(v) \\ _Charles R Greathouse IV_, Mar 20 2017
%Y A284101 Cf. A057622 Initial prime in first sequence of n consecutive primes all congruent to 5 mod 6.
%K A284101 nonn
%O A284101 1,1
%A A284101 _Zak Seidov_, Mar 20 2017
%E A284101 a(9)-a(23) from _Charles R Greathouse IV_, Mar 20 2017