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 1-3 of 3 results.

A092641 Absolute value of difference between counts of uninterrupted runs of 2 primes in A092639 and A092640.

Original entry on oeis.org

0, 3, 6, 15, 29, 117, 500, 1136, 4475, 3065, 8440
Offset: 1

Views

Author

Enoch Haga, Mar 02 2004

Keywords

Examples

			a(2)=3 because in A092639 the count is 2 and in A092640 the count is 5. 5 - 3 = 2.
		

Crossrefs

Formula

Take the absolute value of the difference between counts of runs of 2 primes congruent to 1 mod 4 and 3 mod 4.

Extensions

a(9)-a(11) from Chai Wah Wu, Mar 18 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

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

A093398 Absolute value of difference between counts of uninterrupted runs of 2 nonprimes in A093185 and A093186.

Original entry on oeis.org

1, 0, 3, 2, 43, 85, 42, 36, 3823, 192, 5114, 2797, 148220
Offset: 1

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=3 because in A093185 the count is 33 and in A093186 the count is 36. 36-33=3.
		

Crossrefs

Formula

Take the absolute value of differences between counts of runs of 2 nonprimes congruent to 1 mod 4 and 3 mod 4

Extensions

a(9)-a(13) from Robert Price, May 30 2019
Showing 1-3 of 3 results.