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.

User: Jon Wild

Jon Wild's wiki page.

Jon Wild has authored 66 sequences. Here are the ten most recent ones:

A344488 Numbers that start a product crescendo of record length.

Original entry on oeis.org

1, 2, 3, 7, 47, 181, 1307, 2503, 40973, 46833, 109177, 2885373, 11744311, 192968969, 899988745
Offset: 1

Views

Author

Jon Wild, May 20 2021

Keywords

Comments

A product crescendo is a sequence of successive integers that can be written as products j * k where the j's form a strictly increasing sequence and the k's form a strictly decreasing sequence.
From Jon E. Schoenfield, May 22 2021: (Start)
a(16) <= 13399626241.
Numbers that start long product crescendos, but are not necessarily of record length, are easy to find by testing numbers of the form 1 + m*lcm(1..k) for sufficiently large m and k. E.g., the ones that start at 13399626241 = 1 + 18592*lcm(1..16), 442452890881 = 1 + 36112*lcm(1..17), and 521688126961 = 1 + 2241*lcm(1..19) have lengths 37, 39, and 41 respectively. (End)
The sequence is infinite as for any n >= 0, A038507(n) starts a product crescendo of length >= n. - Rémy Sigrist, May 22 2021

Examples

			181 is in the list because it begins a product crescendo that is longer than any beginning at any smaller number. Here is the crescendo:
    1 * 181  =  181
    2 *  91  =  182
    3 *  61  =  183
    4 *  46  =  184
    5 *  37  =  185
    6 *  31  =  186
   11 *  17  =  187
   47 *   4  =  188
   63 *   3  =  189
   95 *   2  =  190
  191 *   1  =  191
This set of 11 products forms a longer crescendo than the previous record (which started at 47), and is the longest until the set of 13 products it is possible to write starting from 1307 (the next entry in the sequence).
Additional example: the crescendo from 2885373 (length 27) goes:
        1 * 2885373 = 2885373
        2 * 1442687 = 2885374
        5 * 577075  = 2885375
        6 * 480896  = 2885376
       11 * 262307  = 2885377
       19 * 151862  = 2885378
       21 * 137399  = 2885379
       89 * 32420   = 2885380
      859 * 3359    = 2885381
     1458 * 1979    = 2885382
     4817 * 599     = 2885383
    12437 * 232     = 2885384
    19365 * 149     = 2885385
    33551 * 86      = 2885386
    93077 * 31      = 2885387
   131154 * 22      = 2885388
   221953 * 13      = 2885389
   288539 * 10      = 2885390
   320599 * 9       = 2885391
   360674 * 8       = 2885392
   412199 * 7       = 2885393
   480899 * 6       = 2885394
   577079 * 5       = 2885395
   721349 * 4       = 2885396
   961799 * 3       = 2885397
  1442699 * 2       = 2885398
  2885399 * 1       = 2885399

Crossrefs

Cf. A038507.

Programs

  • PARI
    b(n)={if(n==1, 1, my(m=1); for(k=1, oo, fordiv(n+k, d, if(d>m, m=d; break)); if(m==n+k, return(k+1))))}
lista(lim)={my(m=0); for(n=1, lim, my(t=b(n)); if(t > m, print1(n, ", "); m=t))} \\ Andrew Howroyd, May 21 2021

Extensions

a(13)-a(14) from Rémy Sigrist, May 21 2021
a(15) from Jon E. Schoenfield, May 21 2021

A288568 Number of non-isomorphic connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 3, 21, 984, 609423
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on August 31 2016

Keywords

Comments

These counts have been reduced for mirror symmetry. Computed up to n=5 by Jon Wild and Christopher Jones and communicated to N. J. A. Sloane on August 31 2016. Definition corrected Dec 10 2017 thanks to Manfred Scheucher, who has computed same result with Stefan Felsner independently.
The list of arrangements is available online on the Homepage of Pseudocircles (see below) and a detailed description for the enumeration can be found in Arrangements of Pseudocircles: On Circularizability (see below). - Manfred Scheucher, Dec 11 2017
See A250001, the main entry for this problem, for further information.

Links

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568, A296406, A296407-A296412, A006248.

Formula

a(n) = 2^(\Theta(n^2)). (cf. Arrangements of Pseudocircles: On Circularizability)

Extensions

a(6) from Manfred Scheucher, Dec 11 2017

A288567 Number of connected arrangements of n circles in the affine plane, in the sense that the union of the boundaries of the circles is a connected set and every circle intersects all the other circles.

Original entry on oeis.org

1, 1, 1, 3, 21, 980
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild

Keywords

Comments

These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288564 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 2, 11, 183, 30408
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

Arrangements in A288563 that are connected (in the sense that the union of the solid pseudo-circles is a connected set).
These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288563 Number of one-sided arrangements of n pseudo-circles in the affine plane.

Original entry on oeis.org

1, 1, 3, 14, 200, 30630
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288565 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 1, 6, 139, 28643
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

Arrangements in A288559 that are connected, in the sense that the union of the (boundaries of the) pseudo-circles is a connected set.
These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288562 Number of arrangements of n pseudo-circles in the affine plane with the property that every pseudo-circle intersects all the other circles.

Original entry on oeis.org

1, 1, 1, 4, 45, 5108, 4598809
Offset: 0

Views

Author

N. J. A. Sloane, Jun 12 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

Arrangements in A288559 that are connected, with the property that every pseudo-circle intersects all the other pseudo-circles.
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

Extensions

a(6) from Manfred Scheucher, May 09 2018

A288561 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 6, 112, 15528
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

Arrangements in A288559 that are connected, in the sense that the union of the (boundaries of the) pseudo-circles is a connected set.
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288560 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 2, 11, 156, 16782
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

Arrangements in A288559 that are connected (in the sense that the union of the solid pseudo-circles is a connected set).
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A288559 Number of arrangements of n pseudo-circles in the affine plane.

Original entry on oeis.org

1, 1, 3, 14, 173, 16977, 17552169
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.
This sequence is also an upper bound for A250001. - Andrii Shportko, Jun 03 2025

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

Extensions

After consulting with Jon Wild, a(6) added by Andrii Shportko, Jun 03 2025

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

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