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.

A375515 RUNS transform of A375499.

Original entry on oeis.org

2, 3, 3, 7, 8, 12, 24, 20, 4, 36, 48, 24, 60, 72, 76
Offset: 1

Views

Author

N. J. A. Sloane, Aug 18 2024

Keywords

Comments

Also, a(n) is the number of terms equal to n in A375499. - Max Alekseyev, Aug 18 2024

Crossrefs

Cf. A375499.

Extensions

a(11)-a(15) from Max Alekseyev, Aug 18 2024

A373813 a(n) is the smallest number of straight lines needed to intersect all points (k, prime(k)) for k = 1..n.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15
Offset: 1

Views

Author

Rémy Sigrist and N. J. A. Sloane, Aug 18 2024

Keywords

Comments

Dan Asimov asks if the graph is trying to converge to the Cantor (or Devil's Staircase) function. - N. J. A. Sloane, Aug 25 2024

Links

Crossrefs

Cf. A373814 (run lengths), A373810 (same with y(k) = phi(k)), A373811 (similar with y(k) = a(k)), A375499 (same with y(k)=sigma(k)).
See also A376187, A376188, A376190 for single lines.

Extensions

Terms a(19) onward from Max Alekseyev, Aug 18 2024

A373811 a(0) = 0. For n > 0, a(n) is the smallest number of straight lines needed to intersect all points (k, a(k)) for 0 <= k < n.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18
Offset: 0

Views

Author

N. J. A. Sloane, Aug 13 2024, based on an email from Dominic McCarty

Keywords

Comments

The github site of Arthur O'Dwyer has illustrations of many of the small configurations of lines. At his suggestion, I am including his drawings for n = 5, 8, 13, 17, 23, 28, which are just before a(n) increases.

References

  • Dominic McCarty, Email to N. J. A. Sloane, Aug 13 2024.

Links

Crossrefs

See A373812 for the lengths of runs of identical terms.
For minimal sets of lines covering some classic sequences, see A373810, A373813, A375499.

Extensions

a(32)-a(46) from Zachary DeStefano, Aug 14 2024
a(35) corrected and terms a(47) onward added by Max Alekseyev, Aug 15 2024

A373810 a(n) is the smallest number of straight lines needed to intersect all points (k, phi(k)) for k = 1..n (where phi is the Euler totient function A000010).

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17
Offset: 1

Views

Author

Rémy Sigrist and N. J. A. Sloane, Aug 18 2024

Keywords

Links

Crossrefs

Cf. A000010, A375499, A373813, A373815 (RUNS).

Extensions

Terms a(19) onward from Max Alekseyev, Aug 18 2024
Showing 1-4 of 4 results.

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

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