

A093187


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


5



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

1,3


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


EXAMPLE

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


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 *)


CROSSREFS

Cf. A092642, A093183, A093184, A093185, A093186, A093188, A093397, A093398, A093399.
Sequence in context: A300607 A301349 A007035 * A208616 A219169 A292058
Adjacent sequences: A093184 A093185 A093186 * A093188 A093189 A093190


KEYWORD

more,nonn


AUTHOR

Enoch Haga, Mar 30 2004


EXTENSIONS

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


STATUS

approved



