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 1-4 of 4 results.

A092644 Absolute value of difference between counts of uninterrupted runs of 3 primes in A092642 and A092643.

Original entry on oeis.org

0, 0, 3, 2, 18, 30, 8, 943, 2680, 483, 10001
Offset: 1

Views

Author

Enoch Haga, Mar 02 2004

Keywords

Examples

			a(3)=3 because in A092642 the count is 4 and in A092643 the count is 1. 4 - 1 = 3.
		

Crossrefs

Formula

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

Extensions

a(9)-a(11) from Chai Wah Wu, Mar 18 2018

A093399 Absolute value of difference between counts of uninterrupted runs of 3 nonprimes in A093187 and A093188.

Original entry on oeis.org

0, 1, 5, 4, 34, 116, 130, 241, 2187, 3076, 9683, 33067, 133346
Offset: 1

Views

Author

Enoch Haga, Mar 30 2004

Keywords

Examples

			a(3)=5 because in A093187 the count is 10 and in A093188 the count is 5. 10-5=5.
		

Crossrefs

Formula

Take the absolute value of differences between counts of runs of 3 odd nonprimes congruent to 1 mod 4 and 3 mod 4
a(n) = abs(A093187(n) - A093188(n))

Extensions

a(9)-a(13) from Lucas A. Brown, Sep 19 2024

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

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

A092643 Number of consecutive prime runs of 3 primes congruent to 3 mod 4 below 10^n.

Original entry on oeis.org

0, 0, 1, 36, 323, 2480, 20947, 183898, 1621279, 14492365, 131016136
Offset: 1

Views

Author

Enoch Haga, Mar 02 2004

Keywords

Examples

			a(5)=323 because 323 sets of 3 primes occur below 10^5, each run interrupted by a prime congruent to 1 mod 4.
		

Crossrefs

Formula

Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 3 primes occur before interruption by a prime congruent to 1 mod 4.

Extensions

a(9)-a(11) from Chai Wah Wu, Mar 18 2018
Showing 1-4 of 4 results.