A093188 Number of consecutive runs of 3 odd nonprimes congruent to 3 mod 4 below 10^n.

0, 0, 5, 49, 356, 2678, 21085, 166814, 1345812, 11080939, 92699035, 786630700, 6757485506

Offset: 1

Author

Enoch Haga, Mar 30 2004

Keywords

• more
• nonn

Examples

			a(3)=5 because 5 nonprime runs of 3 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.
		

Crossrefs

Cf. A093183, A093184, A093185, A093186, A093187, A093397, A093398, A093399, A092643.

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]]}]]] == 3, AppendTo[lst, Last[s]]], {i, Length[A091113] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}]  (* Robert Price, May 31 2019 *)

Formula

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 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