A093184 Number of consecutive runs of just 1 odd nonprime congruent to 3 mod 4 below 10^n.

0, 4, 76, 1120, 13428, 151342, 1642285, 17405478, 181923798, 1883330510, 19364376037, 198115964781, 2019328569227

Offset: 1

Author

Enoch Haga, Mar 30 2004

Keywords

• more
• nonn

Examples

			a(3)=76 because 76 single nonprime runs occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4
		

Crossrefs

Cf. A093183, A093185, A093186, A093187, A093188, A093397, A093398, A093399, A092637.

Programs

Mathematica

A091113 = Select[4 Range[0, 10^4] + 1, ! PrimeQ[#] &];
A091236 = Select[4 Range[0, 10^4] + 3, ! PrimeQ[#] &];
lst = {}; Do[If[Length[s = Select[A091236, Between[{A091113[[i]], A091113[[i + 1]]}]]] == 1, AppendTo[lst, s]], {i, Length[A091113] - 1}]; Table[Count[Flatten[lst], x_ /; x < 10^n], {n, 4}]  (* Robert Price, May 30 2019 *)

Formula

Generate the odd nonprime sequence with nonprimes labeled 1 mod 4 or 3 mod 4. Add count of nonprimes to sequence if just 1 nonprime congruent to 3 mod 4 occurs before interruption of a nonprime congruent to 1 mod 4.

Extensions

a(9)-a(13) from Bert Dobbelaere, Dec 19 2018