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%I #11 Jul 20 2016 02:53:04
%S 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,
%T 26,33,25,34,24,35,23,36,22,37,21,38,47,48,46,49,45,50,44,51,43,52,42,
%U 53,41,54,40,55,39,56,72,73,71,74,70,75,69,76,68,77,67,78,66,79,65,80
%N A permutation of the natural numbers in groups of 2*k^2, k=1,2,....
%C 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:
%C ...........................1...2.........................
%C ...........................3...4.........................
%C ..................5..6..7..8...9.10.11.12................
%C .................13.14.15.16..17.18.19.20................
%C ..21.22.23.24.25.26.27.28.29..30.31.32.33.34.35.36.37.38.
%C ..39.40.41.42.43.44.45.46.47..48.49.50.51.52.53.54.55.56.
%C 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.
%H Michael De Vlieger, <a href="/A172002/b172002.txt">Table of n, a(n) for n = 1..10680</a> (First 76 rows)
%H Anonymous, <a href="http://www.webelements.com/nexus/Janet_Periodic_Table">Janet periodic table</a>, Web Elements Chemistry
%H Anonymous, <a href="http://www.meta-synthesis.com/webbook/35_pt/pt.html">Periodic Table: Formulations</a>, Chemogenesis web book
%H Albert Tarantola, <a href="http://www.ipgp.fr/~tarantola/Files/Professional/Mendeleev/">PSE of Elements (Janet form)</a>.
%t 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 *)
%K nonn
%O 1,2
%A _Paul Curtz_, Jan 22 2010
%E Edited by _R. J. Mathar_, Mar 02 2010
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