A093185 Number of consecutive runs of 2 odd nonprimes congruent to 1 mod 4 below 10^n.

1, 4, 33, 309, 2805, 25566, 230989, 2106529, 19303539, 177948527, 1649241049, 15360074924, 143682925080

Offset

1,2

Links

Table of n, a(n) for n=1..13.

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 1 mod 4 occur before interruption of a nonprime congruent to 3 mod 4.

Example

a(3)=33 because 33 nonprime runs of 2 occur below 10^3, each run interrupted by a nonprime congruent to 3 mod 4

Mathematica

A091113 = Select[4 Range[0, 10^4] + 1, ! PrimeQ[#] &];
A091236 = Join[{0}, Select[4 Range[0, 10^4] + 3, ! PrimeQ[#] &]];
lst = {}; Do[If[Length[s = Select[A091113, Between[{A091236[[i]], A091236[[i + 1]]}]]] == 2, AppendTo[lst, Last[s]]], {i, Length[A091236] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}]  (* Robert Price, May 30 2019 *)

Crossrefs

Cf. A093183 A093184 A093186 A093187 A093187 A093188 A093397 A093398 A093399 A092639.

Sequence in context: A123780 A054371 A028576 * A198006 A339654 A347749

Adjacent sequences: A093182 A093183 A093184 * A093186 A093187 A093188

Keyword

nonn,more

Author

Enoch Haga, Mar 30 2004

Extensions

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

Status

approved