A172002 A permutation of the natural numbers in groups of 2*k^2, k=1,2,....

1, 2, 3, 4, 8, 9, 7, 10, 6, 11, 5, 12, 16, 17, 15, 18, 14, 19, 13, 20, 29, 30, 28, 31, 27, 32, 26, 33, 25, 34, 24, 35, 23, 36, 22, 37, 21, 38, 47, 48, 46, 49, 45, 50, 44, 51, 43, 52, 42, 53, 41, 54, 40, 55, 39, 56, 72, 73, 71, 74, 70, 75, 69, 76, 68, 77, 67, 78, 66, 79, 65, 80

Offset: 1

Author

Paul Curtz, Jan 22 2010

Keywords

• nonn

Comments

The idea is based on the Janet table of the elements (see A138509 and A171710). Arrange the atomic numbers as if the rows of the table were centered. There are two rows with 2 =2*1^2 elements, 2 rows with 8=2*2^2 elements, 2 rows with 18=2*3^2 elements, and this is extended infinitely by adding 2 rows with 2*k^2 elements (see A137583), incrementing k:

...........................1...2.........................

...........................3...4.........................

..................5..6..7..8...9.10.11.12................

.................13.14.15.16..17.18.19.20................

..21.22.23.24.25.26.27.28.29..30.31.32.33.34.35.36.37.38.

..39.40.41.42.43.44.45.46.47..48.49.50.51.52.53.54.55.56.

The sequence is obtained by reading the numbers in each of the rows (top-down), starting with the center left column, then the center right column, and then alternating from the left to the right, increasing the distance to the center until all 2*k^2 numbers of the block are exhausted.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10680 (First 76 rows)
• Anonymous, Janet periodic table, Web Elements Chemistry
• Anonymous, Periodic Table: Formulations, Chemogenesis web book
• Albert Tarantola, PSE of Elements (Janet form).

Programs

Mathematica

Table[(Riffle[Reverse@ #, Length@ # + #] &@ Range[Ceiling[n/2]^2]) + (# + 1) (3 + 2 #^2 + 4 # - 3 (-1)^#)/12 &[n - 1], {n, 7}] // Flatten (* Michael De Vlieger, Jul 19 2016, after Vincenzo Librandi at A168380 *)

Extensions

Edited by R. J. Mathar, Mar 02 2010