A199426 - OEIS

%I #10 Feb 23 2019 04:22:27

%S 1,2,3,4,5,6,7,10,9,8,11,12,13,14,15,18,17,16,19,20,21,22,23,24,25,30,

%T 29,28,27,26,31,32,33,36,35,34,37,38,39,40,41,42,43,48,47,46,45,44,49,

%U 50,51,54,53,52,55,56,57,58,59,60,61,62,63,70,69,68,67,66,65,64

%N Janet helicoidal classification of the periodic table.

%C A permutation of the natural numbers up to 120 (Janet table; in OEIS Wiki, Periodic table). Or more (extension).

%C Janet explicitly published his table in reference (1), leaflet 7. This was a consequence of his helicoidal classification of the periodic table created with four tangential increasing cylinders on which the numbers are written (2), leaflet 3, (for the first 3 cylinders):

%C (A)                            25 26             43 44

%C                                24 27             42 45

%C         7  8       15 16       23 28 33 34       41 46 51 52

%C         6  9       14 17       22 29 32 35       40 47 50 53

%C 1 2 3 4 5 10 11 12 13 18 19 20 21 30 31 36 37 38 39 48 49 54 55 56.

%C A boustrophedon path is used. 1 increases, 2 decreases.

%C a(n) is the vertical terms taken from bottom to top.

%C By 2 consecutive verticals the numbers of the terms are 2,2,6,2,6,2,10,6,2,... = A167268.

%D (1) Charles Janet, Essais de classification hélicoidale des éléments chimiques, avril 1928, N 3, Beauvais, 2+104 pages, 4 leaflets (3 to 7).

%D (2) Charles Janet, La classification hélicoidale des éléments chimiques, novembre 1928, N 4, Beauvais, 2+80 pages, 10 leaflets.

%F A167268/2 = 1,1,3,1,3,1,5,3,1,5,3,1,... = b(n). b(n) repeated is every term of A167268 shared in 2 equal parts: 1,1,1,1,3,3,1,1,5,5,3,3,1,1,... = c(n), distribution of verticals of (A).

%F a(n) is created by mixed increasing 1, 3,  5,6,7, 11, 13,14,15,   via b(n) (or both via c(n))

%F and                                 2, 4, 10,9,8, 12, 18,17,16, (separately decreasing from right to left for 2, 4, 8,9,10, 11, 16,17,18).

%K nonn

%O 1,2

%A _Paul Curtz_, Nov 06 2011