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A354590 a(n) is the first prime that is the start of a sequence of exactly n consecutive primes that are in A354589.

%I A354590 #20 Aug 23 2022 10:17:54
%S A354590 11,47,251,9431,191,19457,280627,2213,1006253,9129563,66945301,
%T A354590 184171621,726512053,2732087209,10206934519,59883612989,25650350371
%N A354590 a(n) is the first prime that is the start of a sequence of exactly n consecutive primes that are in A354589.
%e A354590 a(3) = 251 because the 4 primes starting with 251 are 251, 257, 263, 269, and 251, 257 and 263 are in A354589 but 269 is not; and 251 is the least prime for which this works.
%p A354590 P:= select(isprime, [seq(i,i=1..10^7,2)]):
%p A354590 nP:= nops(P);
%p A354590 P10:= P mod 10:
%p A354590 s:= 0: V:= Vector(10):
%p A354590 for i from 1 to nP-3 do
%p A354590   if convert(P10[i..i+3],set) = {1,3,7,9} then s:= s+1
%p A354590   else
%p A354590     if s > 0 and s <= 10 and V[s] = 0 then V[s]:= P[i-s] fi;
%p A354590     s:= 0
%p A354590   fi
%p A354590 od:
%p A354590 convert(V, list);
%Y A354590 Cf. A007652, A354589.
%K A354590 nonn,more,base
%O A354590 1,1
%A A354590 _J. M. Bergot_ and _Robert Israel_, Aug 18 2022
%E A354590 a(11)-a(14) from _Michael S. Branicky_, Aug 18 2022
%E A354590 a(15)-a(17) from _Michael S. Branicky_, Aug 20 2022