A093184
Number of consecutive runs of just 1 odd nonprime congruent to 3 mod 4 below 10^n.
Original entry on oeis.org
0, 4, 76, 1120, 13428, 151342, 1642285, 17405478, 181923798, 1883330510, 19364376037, 198115964781, 2019328569227
Offset: 1
a(3)=76 because 76 single nonprime runs occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4
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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]]}]]] == 1, AppendTo[lst, s]], {i, Length[A091113] - 1}]; Table[Count[Flatten[lst], x_ /; x < 10^n], {n, 4}] (* Robert Price, May 30 2019 *)
A093188
Number of consecutive runs of 3 odd nonprimes congruent to 3 mod 4 below 10^n.
Original entry on oeis.org
0, 0, 5, 49, 356, 2678, 21085, 166814, 1345812, 11080939, 92699035, 786630700, 6757485506
Offset: 1
a(3)=5 because 5 nonprime runs of 3 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.
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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 *)
A093185
Number of consecutive runs of 2 odd nonprimes congruent to 1 mod 4 below 10^n.
Original entry on oeis.org
1, 4, 33, 309, 2805, 25566, 230989, 2106529, 19303539, 177948527, 1649241049, 15360074924, 143682925080
Offset: 1
a(3)=33 because 33 nonprime runs of 2 occur below 10^3, each run interrupted by a nonprime congruent to 3 mod 4
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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 *)
A093186
Number of consecutive runs of 2 odd nonprimes congruent to 3 mod 4 below 10^n.
Original entry on oeis.org
0, 4, 36, 307, 2848, 25651, 231031, 2106565, 19307362, 177948719, 1649246163, 15360077721, 143683073300
Offset: 1
a(3)=36 because 36 nonprime runs of 2 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.
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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 *)
A093187
Number of consecutive runs of 3 odd nonprimes congruent to 1 mod 4 below 10^n.
Original entry on oeis.org
0, 1, 10, 53, 390, 2794, 21215, 167055, 1347999, 11084015, 92708718, 786663767, 6757618852
Offset: 1
a(3)=10 because 10 nonprime runs of 3 occur below 10^3, each run interrupted by a nonprime congruent to 3 mod 4.
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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 *)
Showing 1-5 of 5 results.