A093186 Number of consecutive runs of 2 odd nonprimes congruent to 3 mod 4 below 10^n.

0, 4, 36, 307, 2848, 25651, 231031, 2106565, 19307362, 177948719, 1649246163, 15360077721, 143683073300

Offset: 1

Author

Enoch Haga, Mar 30 2004

Keywords

• nonn
• more

Examples

			a(3)=36 because 36 nonprime runs of 2 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.
		

Crossrefs

Cf. A093183 A093184 A093185 A093187 A093188 A093397 A093398 A093399 A092640.

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]]}]]] == 2, AppendTo[lst, Last[s]]], {i, Length[A091113] - 1}]; Table[Count[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 2 nonprimes congruent to 3 mod 4 occur before interruption of a nonprime congruent to 1 mod 4

Extensions

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