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

Janet published 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):

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

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)..

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_Paul Curtz (bpcrtz(AT)free.fr), _, Nov 06 2011

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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, 29, 28, 27, 26, 25, 31, 32, 33, 36, 35, 34, 37, 38, 39, 40, 41, 42, 43, 48, 47, 46, 45, 44, 49, 50, 51, 54, 53, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 70, 69, 68, 67, 66, 65, 64

allocated for Paul CurtzJanet helicoidal classification of the periodic table.

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, 29, 28, 27, 26, 25, 31, 32, 33, 36, 35, 34, 37, 38, 39, 40, 41, 42, 43, 48, 47, 46, 45, 44, 49, 50, 51, 54, 53, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 70, 69, 68, 67, 66, 65, 64

1,2

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

Janet published explicitly 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):

(A) 25 26 43 44

24 27 42 45

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

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

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

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

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

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

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

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

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)..

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

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).

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Paul Curtz (bpcrtz(AT)free.fr), Nov 06 2011

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allocated for Paul Curtz

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