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%I #16 Mar 23 2023 07:59:25
%S 56197,342037,464941,534637,637327,651169,698239,774919,823789,
%T 1142083,1260757,1382167,1498789,1614637,1625707,1814599,1881811,
%U 2213389,2228509,2597869,2602783,2821141,2833309,2980531,3009043,3019339,3056959,3083869,3185551,3204739,3300139,3593917,3837727
%N Primes p such that the six consecutive primes starting at p are congruent to 1,2,4,5,7,8 (mod 9) in that order.
%H Robert G. Wilson v, <a href="/A360188/b360188.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 56197 since it is the least prime that is the first of six consecutive primes, {56197, 56207, 56209, 56237, 56239, 56249}, which are congruent to {1, 2, 4, 5, 7, 8} (mod 9).
%e 217 is not a term because [217, 223, 227, 229, 233, 239] (mod 9) = [1, 7, 2, 4, 8, 5].
%t p = 19; lst = {}; Do[ While[ !PrimeQ[p] || Mod[ NextPrime[p], 9] != 2 || Mod[NextPrime[p, 2], 9] != 4 || Mod[NextPrime[p, 3], 9] != 5 || Mod[NextPrime[p, 4], 9] != 7 || Mod[NextPrime[p, 5], 9] != 8, p += 18]; AppendTo [lst, p]; p += 18, {33}]; lst
%Y Cf. A038194.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert G. Wilson v_, Jan 29 2023