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.

A091318 Lengths of runs of 1's in A039702.

Original entry on oeis.org

1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 4, 2, 1, 1, 2, 2, 3, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 3, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 3
Offset: 1

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Author

Enoch Haga, Feb 22 2004

Keywords

Comments

Number of primes congruent to 1 mod 4 in sequence before interruption by a prime 3 mod 4.

Examples

			a(8)=3 because this is the sequence of primes congruent to 1 mod 4: 89, 97, 101. The next prime is 103, a prime 3 mod 4.

References

  • Enoch Haga, Exploring prime numbers on your PC and the Internet with directions to prime number sites on the Internet, 2001, pages 30-31. ISBN 1-885794-17-7.

Links

Crossrefs

Cf. A002144, A002145, A039702, A091267, A091237.

Programs

  • Mathematica
    t = Length /@ Split[Table[Mod[Prime[n], 4], {n, 2, 400}]]; Most[Transpose[Partition[t, 2]][[2]]] (* T. D. Noe, Sep 21 2012 *)

Formula

Count primes congruent to 1 mod 4 in sequence before interruption by a prime divided by 4 with remainder 3.

A091237 Lengths of runs in A039702.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 4, 1, 1, 1, 1, 2, 3, 7, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 3, 2, 2, 2, 1, 3, 4
Offset: 1

Views

Author

N. J. A. Sloane, Feb 22 2004

Keywords

Comments

Lengths of runs, where a run is a succession of primes that are congruent mod 4.
In other words, RUNS transform of A039702. If the two initial 1's are omitted, this is the RUNS transform of A100672. - N. J. A. Sloane, Jan 11 2025

Links

Crossrefs

Cf. A039702, A091318, A091267, A100672.

Programs

  • Mathematica
    Most[Length /@ Split[Table[Mod[Prime[n], 4], {n, 200}]]] (* T. D. Noe, Sep 21 2012 *)

Extensions

More terms from David Wasserman, Feb 28 2006

A091295 (Number of primes == 3 mod 4 less than 10^n) - (number of primes == 1 mod 4 less than 10^n).

Original entry on oeis.org

1, 2, 7, 10, 25, 147, 218, 446, 551, 5960, 14252, 63337, 118472, 183457, 951700, 3458334, 6284060, 2581691, 80743228, 259753425
Offset: 1

Views

Author

Enoch Haga, Feb 23 2004

Keywords

Examples

			a(1) = 1 because below 10^1 3 and 7 are 3 mod 4 and 5 is 1 mod 4 and the difference is 2-1=1.

References

  • Hans Riesel, Prime Numbers and Computer Methods for Factorization, 2nd ed., Birkhauser, The distribution of primes between the two series 4n+1 and 4n+3, pages 73-77, with graphs.

Links

Crossrefs

Cf. A091098, A091099. A002144, A002145, A091318, A091267.

Formula

a(n) = A091099(n) - A091098(n) = A093153(n) + 1. [Max Alekseyev, May 17 2009]

Extensions

a(17)-a(20) from Marc Deleglise, Jun 28 2007
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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