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%I #22 Dec 03 2023 10:36:52
%S 18,74,4386,4505,9314,10357,21095,29621,38784,102463,105200,116134,
%T 163300,179967,186918,210515,252830,348709,354022,362345,396820,
%U 400915,431568,438862,457748,464118,470852,477341,493070
%N Numbers n such that numbers 30(n+k) + 1 are prime for k=0..5.
%C Numbers n through n+5 are terms in A111175. There are no cases of 7 consecutive numbers in A111175.
%C All terms are congruent to 4 mod 7.
%H Robert Israel, <a href="/A284659/b284659.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#primes_AP">Index entries for primes in AP</a>
%e a(1)=18 because 1 + 30*k for k=18..23 are 541, 571, 601, 631, 661, 691 all primes: A000040(k) for k={100, 105, 110, 115, 121, 125}.
%p filter:= t -> andmap(isprime, [seq(30*(t+k)+1, k=0..5)]):
%p select(filter, [seq(seq(77*k + i,i=[18,39,53,60,74]),k=0..10000)]); # _Robert Israel_, Apr 04 2017
%t Select[Range[18, 1000000, 7], PrimeQ[1 + 30*#] && PrimeQ[1 + 30*(# + 1)] && PrimeQ[1 + 30*(# + 2)] && PrimeQ[1 + 30*(# + 3)] && PrimeQ[1 + 30*(# + 4)] && PrimeQ[1 + 30*(# + 5)] &]
%t Select[Range[4,10^6,7],AllTrue[30(#+Range[0,5])+1,PrimeQ]&] (* _Harvey P. Dale_, Dec 03 2023 *)
%Y Cf. A111175, A132230.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 31 2017
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