A093187 Number of consecutive runs of 3 odd nonprimes congruent to 1 mod 4 below 10^n.

0, 1, 10, 53, 390, 2794, 21215, 167055, 1347999, 11084015, 92708718, 786663767, 6757618852

Offset: 1

Author

Enoch Haga, Mar 30 2004

Keywords

• more
• nonn

Examples

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

Crossrefs

Cf. A092642, A093183, A093184, A093185, A093186, A093188, A093397, A093398, A093399.

Programs

Mathematica

Accumulate@ Table[Length@ SequencePosition[Range[10^n + 1, 10^(n + 1) - 1, 2] /. {p_ /; PrimeQ@ p -> Nothing, k_ /; Mod[k, 4] == 1 -> 1, k_ /; Mod[k, 4] == 3 -> 3}, {1, 1, 1, 3}], {n, 0, 6}] (* Michael De Vlieger, Jan 02 2017 *)

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

Extensions

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