cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A093397 Absolute value of difference between counts of uninterrupted runs of single nonprimes in A093183 and A093184.

Original entry on oeis.org

0, 1, 2, 6, 9, 31, 88, 205, 1636, 2884, 4569, 30270, 14874
Offset: 1

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=2 because in A093183 the count is 74 and in A093184 the count is 76. 76-74=2.

Crossrefs

Cf. A093183 A093184 A092636 A092637 A092638.

Formula

Take the absolute value of differences between counts of runs of single nonprimes congruent to 1 mod 4 and 3 mod 4

Extensions

a(9)-a(13) from 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

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=76 because 76 single nonprime runs occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4

Crossrefs

Cf. A093183, A093185, A093186, A093187, A093188, A093397, A093398, A093399, A092637.

Programs

  • Mathematica
    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 *)

Formula

Generate the odd nonprime sequence with nonprimes labeled 1 mod 4 or 3 mod 4. Add count of nonprimes to sequence if just 1 nonprime congruent to 3 mod 4 occurs before interruption of a nonprime congruent to 1 mod 4.

Extensions

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

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

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=5 because 5 nonprime runs of 3 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.

Crossrefs

Cf. A093183, A093184, A093185, A093186, A093187, A093397, A093398, A093399, A092643.

Programs

  • Mathematica
    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 *)

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

Extensions

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

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

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

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

Crossrefs

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

Programs

  • 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 *)

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.

Extensions

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

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

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=36 because 36 nonprime runs of 2 occur below 10^3, each run interrupted by a nonprime congruent to 1 mod 4.

Crossrefs

Cf. A093183 A093184 A093185 A093187 A093188 A093397 A093398 A093399 A092640.

Programs

  • Mathematica
    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 *)

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

Extensions

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

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

Views

Author

Enoch Haga, Mar 30 2004

Keywords

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
Showing 1-6 of 6 results.

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