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A354177 Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11).

%I A354177 #38 Oct 09 2022 21:20:04
%S A354177 2,82799,406661,447779,490019,596279,617971,654931,790781,1286969,
%T A354177 1532291,1543357,1775831,1916939,1932911,2220539,2240977,2298749,
%U A354177 2307989,2376629,2435039,2458139,2513579,2731049,2775599,3093851,3141899,3213839,3294337,3331319,3351251,3366497,3645193,3689149,3733259,3781153,3981331
%N A354177 Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11).
%C A354177 All first differences except for 82799 - 2 = 82797 are multiples of 22.
%e A354177 The four consecutive primes {82799, 82811, 82813, 82837} are congruent to {2, 3, 5, 7} (mod 11).
%p A354177 R:= 2: count:= 1:
%p A354177 for p from 13 by 22 while count < 37 do
%p A354177   if not isprime(p) then next fi;
%p A354177   q:= nextprime(p); if q mod 11 <> 3 then next fi;
%p A354177   q:= nextprime(q); if q mod 11 <> 5 then next fi;
%p A354177   q:= nextprime(q); if q mod 11 = 7 then
%p A354177      count:= count+1; R:= R,p fi
%p A354177 od:
%p A354177 R; # _Robert Israel_, Sep 14 2022
%t A354177 s = {2}; p1=7; Do[p1 = NextPrime[p1]; p2 = NextPrime[p1]; p3 = NextPrime[p2]; p4 = NextPrime[p3]; If[{2, 3, 5, 7} == Mod[{p1, p2, p3, p4}, 11], AppendTo[s, p1]], {10^6}]; s
%Y A354177 Subsequence of A167134.
%K A354177 nonn
%O A354177 1,1
%A A354177 _Zak Seidov_, Sep 09 2022