A093183
Number of consecutive runs of just 1 odd nonprime congruent to 1 mod 4 below 10^n.
Original entry on oeis.org
0, 3, 74, 1114, 13437, 151311, 1642197, 17405273, 181925434, 1883327626, 19364371468, 198115934511, 2019328584101
Offset: 1
a(3) = 74 because 74 single nonprime runs occur below 10^3, each run interrupted by a nonprime congruent to 3 mod 4.
Below 10^2 = 100, there are only a(2) = 3 isolated odd nonprimes congruent to 1 mod 4: 33, 57 and 93. (Credits: _Peter Munn_, SeqFan list.) - _M. F. Hasler_, Sep 30 2018
-
A014076 := proc(n)
option remember;
if n = 1 then
1;
else
for a from procname(n-1)+2 by 2 do
if not isprime(a) then
return a;
end if;
end do:
end if;
end proc:
isA091113 := proc(n)
option remember;
if modp(n,4) = 1 and not isprime(n) then
true;
else
false;
end if;
end proc:
isA091236 := proc(n)
option remember;
if modp(n,4) = 3 and not isprime(n) then
true;
else
false;
end if;
end proc:
ct := 0 :
n := 1 :
for i from 2 do
odnpr := A014076(i) ;
prev := A014076(i-1) ;
nxt := A014076(i+1) ;
if isA091113(odnpr) and isA091236(prev) and isA091236(nxt) then
ct := ct+1 ;
end if;
if odnpr< 10^n and nxt >= 10^n then
print(n,ct) ;
n := n+1 ;
end if;
end do: # R. J. Mathar, Oct 02 2018
-
A091113 = Select[4 Range[0, 10^5] + 1, ! PrimeQ[#] &];
A091236 = Select[4 Range[0, 10^5] + 3, ! PrimeQ[#] &];
lst = {}; Do[If[Length[s = Select[A091113,Between[{A091236[[i]], A091236[[i + 1]]}]]] == 1, AppendTo[lst, s]], {i, Length[A091236] - 1}]; Table[Count[Flatten[lst], x_ /; x < 10^n], {n, 5}] (* Robert Price, May 30 2019 *)
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
-
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.
-
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
-
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.
-
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.
-
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 1-6 of 6 results.
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