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 1-7 of 7 results.

A168234 A138100(n) + A168142(n).

Original entry on oeis.org

3, 3, 13, 13, 13, 13, 13, 13, 13, 13, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 171, 171, 171, 171, 171, 171, 171
Offset: 1

Views

Author

Paul Curtz, Nov 21 2009

Keywords

Comments

A138100 counts upwards in blocks of 2*k^2 numbers, restarting from 1,5,21,57,.. = A166464(k-1) = (2*k+1)*(2*k^2-4*k+3)/3, k>=1.
A168142 counts downwards in blocks of 2*k^2 numbers, restarting from 2*k^2, k>=1.
In consequence, the sequence here contains 2*k^2 copies of the number 1+2*k*(1+2*k^2)/3 = 1+A035597(k), k>=1,
where the sequence A035597 is a bisection of A168380.

Crossrefs

Cf. A134984, A138725, A168208.

Extensions

Edited by R. J. Mathar, Feb 15 2010

A335105 Irregular triangle read by rows in which row n lists the partial sums of shell numbers and respective number of electrons for all occupied shells of the n-th element of the periodic table of the elements.

Original entry on oeis.org

1, 2, 1, 3, 1, 3, 5, 6, 1, 3, 5, 7, 1, 3, 5, 7, 9, 10, 1, 3, 5, 7, 9, 11, 1, 3, 5, 7, 9, 12, 1, 3, 5, 7, 9, 13, 1, 3, 5, 7, 9, 14, 1, 3, 5, 7, 9, 15, 1, 3, 5, 7, 9, 15, 18, 19, 1, 3, 5, 7, 9, 15, 18, 20, 1, 3, 5, 7, 9, 15, 18, 20, 23, 24, 1, 3, 5, 7, 9, 15, 18, 20, 23, 25
Offset: 1

Views

Author

David Williams, May 23 2020

Keywords

Comments

The rows provide a way to distinguish the elements.
Electron Configurations for elements after Nobelium (atomic number 102), whose configuration of [RN] 5f14 7s2 comprises the last row of sequence, are at present unknown (see CRC Handbook in References).

Examples

			Lithium 1s2 2s1
        1+2+2+1
        1,3,5,6
Thus:
Hydrogen  1s1           1,2
Helium    1s2           1,3
Lithium   1s2 2s1       1,3,5,6
Beryllium 1s2 2s2       1,3,5,7
Boron     1s2 2s2 2p1   1,3,5,7,9,10

References

  • Darleane C. Hoffman, Diana M. Lee, and Valeria Pershina, Transactinides and Future Elements, in Morss; Edelstein, Norman M.; Fuger, Jean (eds.). The Chemistry of Actinide and Transactinide Elements (3rd ed.). Dordrecht, The Netherlands (2006).
  • Catherine E. Housecroft and Alan G. Sharpe, Inorganic Chemistry (5th ed.). Pearson Education Limited. Harlow, England. (2018).
  • John R. Rumble (ed.), CRC Handbook of Chemistry and Physics, 100th edition. CRC Press. Boca Raton, Florida, 2019; Section 1, Electron Configuration and Ionization Energy of Neutral Atoms in the Ground State.

Links

Crossrefs

Cf. A080915, A168208.

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.

A333662 Number of electrons per shell in element Z=n expressed as a 32-bit unsigned integer.

Original entry on oeis.org

1, 2, 6, 10, 14, 18, 22, 26, 30, 34, 98, 162, 226, 290, 354, 418, 482, 546, 2594, 4642, 4706, 4770, 4834, 2914, 4962, 5026, 5090, 5154, 3234, 5282, 7330, 9378, 11426, 13474, 15522, 17570, 148642, 279714, 281762, 283810
Offset: 1

Views

Author

Zachary Russ, Sep 02 2020

Keywords

Comments

This is a memory-efficient way of encoding the number of electrons per shell of all known elements.

Examples

			  |-----|------------|------------|----------------------------------------|
  |     |            |            |               a(n) [bin]               |
  |  n  | a(n) [dec] | a(n) [hex] |           Electrons per Shell          |
  |     |            |            |  Q  |  P  |   O  |  N   |  M  |  L | K |
  |-----|------------|------------|-----|-----|------|------|-----|----|---|
  |   1 |          1 | 0x00000001 | 0000 00000 000000 000000 00000 0000 01 |
  |   2 |          2 | 0x00000002 | 0000 00000 000000 000000 00000 0000 10 |
  |   3 |          6 | 0x00000006 | 0000 00000 000000 000000 00000 0001 10 |
  |   4 |         10 | 0x0000000a | 0000 00000 000000 000000 00000 0010 10 |
  |   5 |         14 | 0x0000000e | 0000 00000 000000 000000 00000 0011 10 |
  |   6 |         18 | 0x00000012 | 0000 00000 000000 000000 00000 0100 10 |
  |  .  |     .      |      .     |                    .                   |
  |  .  |     .      |      .     |                    .                   |
  |  .  |     .      |      .     |                    .                   |
  | 113 |  960562338 | 0x394104a2 | 0011 10010 100000 100000 10010 1000 10 |
  | 114 | 1228997794 | 0x494104a2 | 0100 10010 100000 100000 10010 1000 10 |
  | 115 | 1497433250 | 0x594104a2 | 0101 10010 100000 100000 10010 1000 10 |
  | 116 | 1765868706 | 0x694104a2 | 0110 10010 100000 100000 10010 1000 10 |
  | 117 | 2034304162 | 0x794104a2 | 0111 10010 100000 100000 10010 1000 10 |
  | 118 | 2302739618 | 0x894104a2 | 1000 10010 100000 100000 10010 1000 10 |
  |-----|------------|------------|----------------------------------------|

Links

Crossrefs

Cf. A333997, A168208, A093907.

A333997 Number of electrons per subshell in element Z=n expressed as a 56-bit unsigned integer.

Original entry on oeis.org

1, 2, 6, 10, 26, 42, 58, 74, 90, 106, 234, 362, 874, 1386, 1898, 2410, 2922, 3434, 68970, 134506, 138602, 142698, 146794, 89450, 154986, 159082, 163178, 167274, 109930, 175466, 437610, 699754, 961898, 1224042, 1486186, 1748330
Offset: 1

Views

Author

Zachary Russ, Sep 05 2020

Keywords

Comments

This is a memory-efficient way of encoding the number of electrons per subshell of all known elements.

Examples

			  |-----|----------------------------------------------------------------------------|
  |     |                                a(n) [bin]                                  |
  |  n  |                          Electrons per Subshell                            |
  |     |  7p|7s| 6d | 6p|6s| 5f | 5d | 5p|5s| 4f | 4d | 4p|4s| 3d | 3p|3s| 2p|2s|1s |
  |-----|----|--|----|---|--|----|----|---|--|----|----|---|--|----|---|--|---|--|---|
  |   1 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 000 00 01 |
  |   2 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 000 00 10 |
  |   3 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 000 01 10 |
  |   4 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 000 10 10 |
  |   5 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 001 10 10 |
  |   6 | 000 00 0000 000 00 0000 0000 000 00 0000 0000 000 00 0000 000 00 010 10 10 |
  |  .  |                                     .                                      |
  |  .  |                                     .                                      |
  |  .  |                                     .                                      |
  | 113 | 001 10 1010 110 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  | 114 | 010 10 1010 110 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  | 115 | 011 10 1010 110 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  | 116 | 100 10 1010 110 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  | 117 | 101 10 1010 110 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  | 118 | 110 10 1010 011 10 1110 1010 110 10 1110 1010 110 10 1010 110 10 110 10 10 |
  |-----|----------------------------------------------------------------------------|

Links

Crossrefs

Cf. A333662, A168208, A093907.

A217927 Elements of the horizontal ADOMAH periodic table written from right to left, from bottom to top.

Original entry on oeis.org

2, 1, 4, 3, 10, 9, 8, 7, 6, 5, 12, 11, 18, 17, 16, 15, 14, 13, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 36, 35, 34, 33, 32, 31, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 38, 37, 54, 53, 52, 51, 50, 49, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89
Offset: 1

Views

Author

Paul Curtz, Oct 15 2012

Keywords

Comments

We first write a variant of the ADOMAH periodic table:
1 2
5 6 7 8 9 10 3 4
21 22 23 24 25 26 27 28 29 30 13 14 15 16 17 18 11 12
57 to 70 39 40 41 42 43 44 45 46 47 48 31 32 33 34 35 36 19 20 (B)
89 to 102 71 72 73 74 75 76 77 78 79 80 49 50 51 52 53 54 37 38
103104105106107108109110111112 81 82 83 84 85 86 55 56
113114115116117118 87 88
119120
(See A219388).
It could be written vertically.
Differences of (2,4,12,20,38,56,88,120,... = A168380) = 2,8,8,18,18,... = A093907 from a 118 terms table.
The number of elements in the n-th period (2,8,18,32,32,18,8,2) is in A168281. Compare to A093907 = 2,8,8,18,18,32,32,50,...(extension of the Mendeleyev-Moseley-Seaborg table) and A137583 = 2,2,8,8,18,18,32,32. See the possible element 120 in A168208 (which must be clarified).
The horizontal ADOMAH periodic table (2006) is
119120
113114115116117118 87 88
103104105106107108109110111112 81 82 83 84 85 86 55 56
89 to 102 71 72 73 74 75 76 77 78 79 80 49 50 51 52 53 54 37 38 (A)
57 to 70 39 40 41 42 43 44 45 46 47 48 31 32 33 34 35 36 19 20
21 22 23 24 25 26 27 28 29 30 13 14 15 16 17 18 11 12
5 6 7 8 9 10 3 4
1 2
Generally it is written vertically.

References

  • Philip J. Stewart, "Charles Janet, Unrecognized genius of the periodic system", Foundations of Chemistry, January, 2009. ISSN 1386-4238.

Links

Crossrefs

Cf. A137325.

Extensions

Reference given by Jean-François Alcover, Oct 22 2012
Typos corrected in comments by Jean-François Alcover, Nov 16 2012

A319901 List of elements whose electron configuration does not satisfy the Aufbau principle.

Original entry on oeis.org

24, 29, 41, 42, 44, 45, 46, 47, 57, 58, 64, 78, 79, 89, 90, 91, 92, 93, 96, 103
Offset: 1

Views

Author

Jianing Song, Sep 30 2018

Keywords

Comments

Possibly full, but if some period 8 elements were synthesized there may be a lot more terms.

Examples

			...Element.....Atomic number...EC by Aufbau principle.......Actual EC....
Chromium.............24............[Ar]3d4 4s2..........[Ar]3d5 4s1
Copper...............29............[Ar]3d9 4s2..........[Ar]3d10 4s1
Niobium..............41............[Kr]4d3 5s2..........[Kr]4d4 5s1
Molybdenum...........42............[Kr]4d4 5s2..........[Kr]4d5 5s1
Ruthenium............44............[Kr]4d6 5s2..........[Kr]4d7 5s1
Rhodium..............45............[Kr]4d7 5s2..........[Kr]4d8 5s1
Palladium............46............[Kr]4d8 5s2..........[Kr]4d10
Silver...............47............[Kr]4d9 5s2..........[Kr]4d10 5s1
Lanthanum............57............[Xe]4f1 6s2..........[Xe]5d1 6s2
Cerium...............58............[Xe]4f2 6s2..........[Xe]4f1 5d1 6s2
Gadolinium...........64............[Xe]4f8 6s2..........[Xe]4f7 5d1 6s2
Platinum.............78............[Xe]4f14 5d8 6s2.....[Xe]4f14 5d9 6s1
Gold.................79............[Xe]4f14 5d9 6s2.....[Xe]4f14 5d10 6s1
Actinium.............89............[Rn]5f1 7s2..........[Rn]6d1 7s2
Thorium..............90............[Rn]5f2 7s2..........[Rn]6d2 7s2
Protactinium.........91............[Rn]5f3 7s2..........[Rn]5f2 6d1 7s2
Uranium..............92............[Rn]5f4 7s2..........[Rn]5f3 6d1 7s2
Neptunium............93............[Rn]5f5 7s2..........[Rn]5f4 6d1 7s2
Curium...............96............[Rn]5f8 7s2..........[Rn]5f7 6d1 7s2
Lawrencium..........103............[Rn]5f14 6d1 7s2.....[Rn]5f14 7s2 7p1
(EC = electron configuration.)

Links

Crossrefs

Cf. A168208.
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