|
%I #20 Mar 18 2018 17:25:17
%S 0,0,1,15,111,1013,8963,78496,703783,6388533,58446494
%N Number of consecutive prime runs of just 4 primes congruent to 3 mod 4 below 10^n.
%F Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 4 primes occur before interruption by a prime congruent to 1 mod 4.
%e a(5)=111 because 111 sets of 4 primes occur below 10^5, each run interrupted by a prime congruent to 1 mod 4.
%t p1 = p3 = 0; p = 15; s = Mod[{2, 3, 5, 7, 11, 13}, 4]; Do[ While[p < 10^n, If[s == {3, 1, 1, 1, 1, 3}, p1++]; If[s == {1, 3, 3, 3, 3, 1}, p3++]; p = NextPrime@ p; s = Join[ Take[s, -5], {Mod[p, 4]}]]; Print[{p1, p3}], {n, 2, 9}] (* _Robert G. Wilson v_, Sep 30 2011 *)
%Y Cf. A092645, A092647.
%K more,nonn
%O 1,4
%A _Enoch Haga_, Mar 02 2004
%E a(11) from _Chai Wah Wu_, Mar 18 2018
|
