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%I #10 Sep 20 2023 12:24:34
%S 73471,307537,634577,777671,1381141,1886107,1907527,2449327,2505187,
%T 3078431,3110771,3299323,4076477,4088587,4666801,4829257,4930043,
%U 5069567,5209301,5416291,5513941,5711551,6049567,6053627,6217091,7216691,8057867,8352301,8476817,8635717,8821231,8848811,9073819
%N Primes p such that the six consecutive primes starting with p are congruent to {6, 5, 4, 3, 2, 1} (mod 7).
%H Robert Israel, <a href="/A365309/b365309.txt">Table of n, a(n) for n = 1..2000</a>
%e The six consecutive primes starting with a(3) = 634577 are 634577, 634597, 634603, 634609, 634643, 634649, which are congruent to 6, 5, 4, 3, 2, 1 respectively (mod 7).
%p P:= [0$6]: P7:= [0$6]: E:= [seq(i,i=6..1,-1)];
%p R:= NULL: count:= 0: p:= 0:
%p while count < 10 do
%p p:= nextprime(p);
%p P:= [op(P[2..6]),p];;
%p P7:= [op(P7[2..6]),p mod 7];
%p if P7 = E then count:= count+1; R:= R, P[1]; fi
%p od:
%p R;
%t Prime/@SequencePosition[Mod[Prime[Range[610000]],7],{6,5,4,3,2,1}][[;;,1]] (* _Harvey P. Dale_, Sep 20 2023 *)
%Y Cf. A215599.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Aug 31 2023
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