%I #15 Dec 19 2018 14:43:09
%S 0,1,10,53,390,2794,21215,167055,1347999,11084015,92708718,786663767,
%T 6757618852
%N Number of consecutive runs of 3 odd nonprimes congruent to 1 mod 4 below 10^n.
%F Generate the odd nonprime sequence with nonprimes labeled 1 mod 4 or 3 mod 4. Add count of nonprimes to sequence if 3 nonprimes congruent to 1 mod 4 occur before interruption of a nonprime congruent to 3 mod 4.
%e a(3)=10 because 10 nonprime runs of 3 occur below 10^3, each run interrupted by a nonprime congruent to 3 mod 4.
%t Accumulate@ Table[Length@ SequencePosition[Range[10^n + 1, 10^(n + 1) - 1, 2] /. {p_ /; PrimeQ@ p -> Nothing, k_ /; Mod[k, 4] == 1 -> 1, k_ /; Mod[k, 4] == 3 -> 3}, {1, 1, 1, 3}], {n, 0, 6}] (* _Michael De Vlieger_, Jan 02 2017 *)
%Y Cf. A092642, A093183, A093184, A093185, A093186, A093188, A093397, A093398, A093399.
%K more,nonn
%O 1,3
%A _Enoch Haga_, Mar 30 2004
%E a(9)-a(13) from _Bert Dobbelaere_, Dec 19 2018