

A172002


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


14



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
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OFFSET

1,2


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 (topdown), 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).


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 *)


CROSSREFS

Sequence in context: A050324 A211227 A019949 * A274927 A066338 A047453
Adjacent sequences: A171999 A172000 A172001 * A172003 A172004 A172005


KEYWORD

nonn


AUTHOR

Paul Curtz, Jan 22 2010


EXTENSIONS

Edited by R. J. Mathar, Mar 02 2010


STATUS

approved



