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.

A168208 Irregular table of the number of electrons of the n-th element of the PSE in atomic shells, read by rows.

Original entry on oeis.org

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

Views

Author

Paul Curtz, Nov 20 2009

Keywords

Comments

For the n-th element in the periodic system of elements, row n of the table shows the occupancy of the K-shell, then the L-shell, then the M-shell etc.
Row sums are A000027(n). A093907(c) is the maximum number that may appear in column c.
How are rows defined when the n-th element has more than one possible electron configuration? For example, element no. 28 (Nickel) has two electron configurations, namely 2, 8, 16, 2 and 2, 8, 17, 1, and it is disputed which of them is the ground state configuration of Nickel. - Felix Fröhlich, Jun 02 2019

Examples

			From _Felix Fröhlich_, Jun 02 2019: (Start)
Irregular table starts as follows, where Z denotes the atomic number:
  Z  | Element name | Electrons per shell
  -----------------------------------------
   1 | Hydrogen     | 1
   2 | Helium       | 2
   3 | Lithium      | 2, 1
   4 | Beryllium    | 2, 2
   5 | Boron        | 2, 3
   6 | Carbon       | 2, 4
   7 | Nitrogen     | 2, 5
   8 | Oxygen       | 2, 6
   9 | Fluorine     | 2, 7
  10 | Neon         | 2, 8
  11 | Sodium       | 2, 8,  1
  12 | Magnesium    | 2, 8,  2
  13 | Aluminium    | 2, 8,  3
  14 | Silicon      | 2, 8,  4
  15 | Phosphorus   | 2, 8,  5
  16 | Sulfur       | 2, 8,  6
  17 | Chlorine     | 2, 8,  7
  18 | Argon        | 2, 8,  8
  19 | Potassium    | 2, 8,  8, 1
  20 | Calcium      | 2, 8,  8, 2
  21 | Scandium     | 2, 8,  9, 2
  22 | Titanium     | 2, 8, 10, 2
  23 | Vanadium     | 2, 8, 11, 2
  24 | Chromium     | 2, 8, 13, 1
  25 | Manganese    | 2, 8, 13, 2
  26 | Iron         | 2, 8, 14, 2
  27 | Cobalt       | 2, 8, 15, 2
(End)

Links

Crossrefs

Cf. A173642.

Extensions

Redefined as an irregular table by R. J. Mathar, Dec 05 2009
Edited by Felix Fröhlich, Jun 02 2019

A234305 Irregular triangle read by rows. Theoretical distribution of electrons based on the Janet's sequence A167268.

Original entry on oeis.org

1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 5, 2, 2, 6, 2, 2, 6, 1, 2, 2, 6, 2, 2, 2, 6, 2, 1, 2, 2, 6, 2, 2, 2, 2, 6, 2, 3, 2, 2, 6, 2, 4, 2, 2, 6, 2, 5, 2, 2, 6, 2, 6, 2, 2, 6, 2, 6, 1, 2, 2, 6, 2, 6, 2, 2, 2, 6, 2, 6, 2, 1, 2, 2, 6, 2, 6, 2, 2, 2, 2, 6, 2, 6, 2, 3, 2, 2, 6, 2, 6, 2, 4
Offset: 1

Views

Author

Paul Curtz, Jan 02 2014

Keywords

Comments

a(n) is not A173642, a compact Bohr-Stoner model (1924), modified by Charles Janet in 1930. The good distribution is A168208.
Only sequences N16(n) in A234398 are used:
N16(1)= 1 followed by 2's = A040000,
N16(2)= 1, 2, 3, 4, 5, followed by 6's = A101272,
N16(3)= 1 to 9, followed by 10's,
N16(4)= 1 to 13, followed by 14's, etc.
The distribution by rows are in the example.
The N16(n)'s are respectively on columns (hence triangle T)
1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, A002620(n+2)
3, 5, 8, 11, 15, 19, 24, 29, 35, A024206(n+2)
7, 10, 14, 18, 23, 28, 34, A014616(n+3)
13, 17, 22, 27, 33, A004116(n+4)
21, 26, 32,
31, etc.
See A163255.
Antidiagonals give the natural numbers A000027, like rows sums in the example.
A033638=1, 1, 2, 3, 5, 7,... is upon the triangle T.

Examples

			1,      H
2,       He
2, 1,    Li
2, 2,    Be
2, 2, 1,
2, 2, 2,
2, 2, 3,
2, 2, 4,
2, 2, 5,
2, 2, 6,
2, 2, 6, 1,
2, 2, 6, 2,
2, 2, 6, 2, 1,
2, 2, 6, 2, 2,
2, 2, 6, 2, 3,
2, 2, 6, 2, 4,
2, 2, 6, 2, 5,
2, 2, 6, 2, 6,
2, 2, 6, 2, 6, 1,
2, 2, 6, 2, 6, 2,
2, 2, 6, 2, 6, 2, 1,
2, 2, 6, 2, 6, 2, 2,
2, 2, 6, 2, 6, 2, 3, etc.

Crossrefs

Cf. A002061, A002522 (or A160457), A014206, A059100, diagonals of the triangle T. A004526.

A234398 Distribution of the natural numbers using the sequences family mentioned in the comments.

Original entry on oeis.org

1, 2, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 6, 1, 2, 6, 2, 2, 6, 3, 2, 6, 4, 2, 6, 5, 2, 6, 6, 2, 6, 7, 2, 6, 8, 2, 6, 9, 2, 6, 10, 2, 6, 10, 1, 2, 6, 10, 2, 2, 6, 10, 3, 2, 6, 10, 4, 2, 6, 10, 5, 2, 6, 10, 6, 2, 6, 10, 7
Offset: 1

Views

Author

Paul Curtz, Dec 25 2013

Keywords

Comments

Based on A016825=2,6,10,..., the family is
N16(1)=1, followed by 2's =A040000,
N16(2)=1,2,3,4,5, followed by 6's =A101272,
N16(3)=1,2,3,4,5,6,7,8,9, followed by 10's, not in the OEIS,
N16(4)=1,2,3,4,5,6,7,8,9,10,11,12,13, followed by 14's, idem.
The N16(n) gives the successive columns beginning at row 1, 3, 9, 19, ... =A058331.
Sum of every row: n =A000027.
Note that with only N16(1),
1,
2,
2, 1,
2, 2,
2, 2, 1,
2, 2, 2,
2, 2, 2, 1,
2, 2, 2, 2,
2, 2, 2, 2, 1, etc
is A169695(n+1).
A169695(n) corresponds to A028310.

Examples

			1,
2,
2, 1,
2, 2,
2, 3,
2, 4,
2, 5,
2, 6,
2, 6, 1,
2, 6, 2,
2, 6, 3,
2, 6, 4, etc.

Crossrefs

Cf. A173642.
Showing 1-3 of 3 results.

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