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 1-5 of 5 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

A138101 The atomic numbers read along the even-indexed rows of the Janet table of the elements.

Original entry on oeis.org

3, 4, 13, 14, 15, 16, 17, 18, 19, 20, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120
Offset: 1

Views

Author

Paul Curtz, May 03 2008

Keywords

Comments

The union with A138100 gives the first 120 terms of A000027.

Examples

			Starts with 3 and 4 of the 2nd row (Li and Be). Next come 13 to 20 of the 4th row (Al to Ca).

Links

Crossrefs

Cf. A000027, A138100 (odd-indexed rows), A138509 (Left-step Janet periodic table), A137583, A172002.

Programs

  • Mathematica
    Table[Range[2 Ceiling[n/2]^2] + (# + 1) (3 + 2 #^2 + 4 # - 3 (-1)^#)/12 &[n - 1], {n, 2, 8, 2}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)

Extensions

Edited by R. J. Mathar, Oct 07 2009

A168142 Count downwards from 2, then from 8, then from 18, then from ... 2*k^2, k>=1.

Original entry on oeis.org

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

Views

Author

Paul Curtz, Nov 19 2009

Keywords

Comments

Janet's extended enumeration of the periodic table of the elements.
The table is read from the right to the left.

References

  • Charles Janet, La structure du Noyau de l'atome,consideree dans la Classification periodique des elements chimiques, Nov. 1927, N. 2, Beauvais, 67 pages, 3 leafleats, see page 15.
  • Charles Janet, Considerations sur la structure du noyau de l'atome, Dec 1929, N 5, Beauvais, 2+45 pp.,4 leaflets, see leaflets 2 and 3.

Crossrefs

Cf. A138100, A138101, A093907, A137583, A172002.

Programs

  • Mathematica
    Table[Reverse@ Range[2 n^2], {n, 5}] // Flatten (* Michael De Vlieger, Jul 22 2016 *)

Extensions

Edited by R. J. Mathar, Feb 15 2010

A138102 The number 2*k^2 repeated 2*k^2 times, k=1 to 4.

Original entry on oeis.org

2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
Offset: 1

Views

Author

Paul Curtz, May 03 2008

Keywords

Comments

Vaguely related to the number of elements in the Janet table A138102.
Essentially the same as A137575.
a(n)= (A138101=3,4,13,14,15,16,17,) - (A138100=1,2,5,6,7,8,9,) . [From Paul Curtz, Oct 11 2009]

Links

Crossrefs

Cf. A138101, A137325, A137583, A166071, A001105.

Extensions

Edited by R. J. Mathar, Oct 07 2009

A168342 Even atomic numbers in the Janet table of the PSE, read right to left along rows.

Original entry on oeis.org

2, 4, 12, 10, 8, 6, 20, 18, 16, 14, 38, 36, 34, 32, 30, 28, 26, 24, 22, 56, 54, 52, 50, 48, 46, 44, 42, 40, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 120, 118, 116, 114, 112, 110, 108, 106, 104, 102, 100, 98, 96, 94, 92, 90
Offset: 1

Views

Author

Paul Curtz, Nov 23 2009

Keywords

Comments

In the Janet arrangement, the elements appear in groups of twice 2, twice 8,... twice 2*k^2, and are here right-aligned:
...............................1,.2;
...............................3,.4;
.............5,.6,.7,.8,.9,10,11,12;
............13,14,15,16,17,18,19,20;
...28,39.30,31,32,33,34,35,36,37,38;
The even numbers in the table are read top-down, right-to-left and entered into the sequence (which, in consequence, is a permutation of the even numbers.)

Examples

			Skipping each second (i.e., each odd) element in the table, the result is
2;
4;
12,10,8,6;
20,18,16,14;
38,36,34,32,30,28,..
counting down the even numbers restarting at indices provided by A168380.

Links

Crossrefs

Cf. A138100, A138101, A168142.
Showing 1-5 of 5 results.

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