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: Olaf Voß

Olaf Voß's wiki page.

Olaf Voß has authored 14 sequences. Here are the ten most recent ones:

A184409 Total number of missing toothpicks in the holes in the toothpick structure of A182840.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 6, 6, 8, 12, 22, 42, 42, 42, 42, 42, 42, 42, 46, 58, 68, 72, 72, 72, 100, 148, 150, 186, 186, 186, 186, 186, 186, 186, 190, 202, 210, 210, 210, 210, 214, 226, 254, 314, 356, 360, 360, 360, 360, 360, 368, 396, 524, 708, 652, 628, 676, 764, 710, 762, 762, 762, 762, 762, 762, 762, 766
Offset: 0

Views

Author

Olaf Voß, Jan 13 2011

Keywords

Comments

Each connected group of unoccupied lines in the hexagonal structure enclosed by toothpicks counts as a hole.

Examples

			Structure after step 8:
      \_/
    \_/ \_/
  \_/ \_/ \_/
\_/  _/ \_  \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \ / \_/ \ / \
\_/ \_/ \_/ \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \_  \_/  _/ \
  / \_/ \_/ \
    / \_/ \
      / \
There are 6 holes in this structure, in each 1 toothpick is missing, so a(8)=6.

Links

Crossrefs

For number of holes see A184408.

A184408 Number of holes in the toothpick structure of A182840.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 6, 6, 8, 12, 18, 30, 30, 30, 30, 30, 30, 30, 34, 46, 56, 60, 60, 60, 66, 80, 98, 126, 126, 126, 126, 126, 126, 126, 130, 142, 150, 150, 150, 150, 154, 166, 186, 222, 248, 252, 252, 252, 252, 252, 260, 288, 322, 344, 348, 348, 364, 404, 450, 510, 510, 510, 510, 510, 510, 510, 514, 526
Offset: 0

Views

Author

Olaf Voß, Jan 13 2011

Keywords

Comments

Each connected group of unoccupied lines in the hexagonal structure enclosed by toothpicks counts as a hole.

Examples

			Structure after step 8:
      \_/
    \_/ \_/
  \_/ \_/ \_/
\_/  _/ \_  \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \ / \_/ \ / \
\_/ \_/ \_/ \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \_  \_/  _/ \
  / \_/ \_/ \
    / \_/ \
      / \
There are 6 holes in this structure, so a(8)=6.

Links

Crossrefs

For total number of missing toothpicks see A184409.

A178573 Number of exposed endpoints in the toothpick structure of A182840.

Original entry on oeis.org

2, 4, 8, 8, 8, 12, 20, 16, 8, 12, 24, 32, 28, 28, 44, 32, 8, 12, 24, 32, 32, 40, 64, 72, 44, 28, 56, 84, 80, 72, 100, 64, 8, 12, 24, 32, 32, 40, 64, 72, 48, 40, 72, 112, 120, 112, 144, 152, 76, 28, 56, 84
Offset: 1

Views

Author

Olaf Voß, Dec 24 2010

Keywords

Examples

			At stage 1 we place a toothpick anywhere in the plane (for example, in vertical position). There are two exposed endpoints, so a(1)=2.
At stage 2 we place 4 toothpicks: two new toothpicks touching each exposed endpoint. There are now 4 exposed endpoints, so a(2)=4.

Links

A175797 Size of the largest holes in the toothpick structure of A182840 after step n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 12, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 48, 48, 35, 31, 27, 12, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 12, 12, 7, 3, 3, 3, 3
Offset: 0

Views

Author

Olaf Voß, Jan 13 2011

Keywords

Comments

Each connected group of unoccupied lines in the hexagonal structure enclosed by toothpicks counts as a hole.

Examples

			Structure after step 8:
      \_/
    \_/ \_/
  \_/ \_/ \_/
\_/  _/ \_  \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \ / \_/ \ / \
\_/ \_/ \_/ \_/
/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
/ \_  \_/  _/ \
  / \_/ \_/ \
    / \_/ \
      / \
There are 6 holes in this structure, in each 1 toothpick is missing (size=1), so a(8)=1.

Links

Crossrefs

For number of holes see A184408.

A135502 Admirable numbers in the middle of twin primes.

Original entry on oeis.org

12, 30, 42, 102, 138, 270, 282, 618, 642, 822, 1488, 1698, 1878, 2082, 2238, 2382, 2658, 2802, 3462, 3558, 3918, 4638, 4722, 5442, 6198, 6702, 8538, 8598, 9678, 10938, 12162, 12378, 12822, 12918, 13218, 13722, 13758, 13998, 14082, 16062, 17418
Offset: 1

Views

Author

Olaf Voß, Feb 09 2008

Keywords

Comments

Numbers n such that n is admirable, n-1 is prime and n+1 is prime.

Examples

			30 is in the sequence, as 29=30-1 and 31=30+1 are a pair of twin primes.

Links

Crossrefs

Cf. A111592, A001359, A006512.

Programs

  • Mathematica
    Select[Range[18000],MemberQ[Most[Divisors[#]],(DivisorSigma[1,#]-2#)/2]&&AllTrue[#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Sep 11 2023 *)

Formula

A014574 INTERSECT A111592. - R. J. Mathar, Feb 10 2008

A118167 Minimum values of abs(x^x-n!) for given n.

Original entry on oeis.org

0, 0, 1, 2, 3, 93, 464, 1915, 6336, 316224, 2805257, 23139584, 91581111, 3772979200, 77178291200, 1022362697389, 12006689439744, 52812321503747, 4709633119830016, 110533093583273984, 1995008117795780625
Offset: 0

Views

Author

Olaf Voß, Apr 13 2006

Keywords

Examples

			3! = 6, the closest x^x can get to 6 is 2^2, so a(3) = 3! - 2^2 = 2

Crossrefs

Cf. A118168, A118169.

A118168 a(n) = x for which abs(x^x-n!) is minimal.

Original entry on oeis.org

1, 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57, 57, 58, 59
Offset: 0

Views

Author

Olaf Voß, Apr 13 2006

Keywords

Examples

			3! = 6, the closest x^x can get to 6 is 2^2, so a(3) = 2

Crossrefs

Cf. A118167, A118170.

A118170 x for which abs(n^n-x!) is minimal for given n.

Original entry on oeis.org

1, 1, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86
Offset: 0

Views

Author

Olaf Voß, Apr 13 2006

Keywords

Examples

			3^3 = 27, the closest x! can get to 27 is 4!, so a(3) = 4

Crossrefs

Cf. A118168, A118169.

A118169 Minimum values of abs(n^n-x!) for given n.

Original entry on oeis.org

0, 0, 2, 3, 136, 1915, 6336, 460663, 13148416, 91581111, 3772979200, 198133379411, 7608426080256, 52812321503747, 4709633119830016, 316248789972027375, 16013842065532911616, 296760465891270915823, 13494391336411560935424
Offset: 0

Views

Author

Olaf Voß, Apr 13 2006

Keywords

Examples

			3^3 = 27, the closest x! can get to 27 is 4! = 24, so a(3) = 3^3 - 4! = 3

Crossrefs

Cf. A118167, A118170.

Programs

  • Mathematica
    Join[{0,0},With[{fc=Range[200]!},Drop[Flatten[Table[Abs[n^n-Nearest[ fc,n^n]],{n,18}]],2]]] (* Harvey P. Dale, Jan 02 2016 *)

A102821 Numbers n for which the square excess of n-th prime is prime.

Original entry on oeis.org

2, 4, 5, 8, 9, 13, 14, 15, 19, 20, 23, 27, 28, 30, 35, 36, 37, 38, 39, 46, 49, 56, 57, 67, 68, 69, 71, 81, 83, 86, 93, 94, 96, 98, 107, 108, 109, 111, 112, 113, 114, 124, 128, 138, 139, 142, 144, 155, 156, 157, 158, 159, 160, 161, 162, 173, 178, 182, 192, 195, 196, 199
Offset: 0

Views

Author

Olaf Voß, Feb 27 2005

Keywords

Examples

			7 - 2^2 = 3 is the square excess (see A056892) of 7 and it is prime. 7 is the 4th prime, so 4 is in the sequence.

Crossrefs

Cf. A056892.

Programs

  • Mathematica
    Select[Range[200],PrimeQ[Prime[#]-Floor[Sqrt[Prime[#]]]^2]&] (* Harvey P. Dale, Jul 06 2014 *)

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