A199502 From Janet helicoidal classification of the periodic table.

1, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20, 21, 30, 31, 36, 37, 38, 39, 48, 49, 54, 55, 56, 57, 70, 71, 80, 81, 86, 87, 88, 89, 102, 103, 112, 113, 118, 119, 120, 121, 138, 139, 152, 153, 162, 163, 168, 169, 170, 171, 188, 189, 202, 203, 212, 213, 218, 219, 220, 221

Offset: 1

Author

Paul Curtz, Nov 07 2011

Keywords

• nonn

Comments

In A199426, we saw how Janet discovered

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 57

a(n) is the last row.

a(n+1) - a(n) = 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 9, 1, 5, 1, 1, 1, 9, 1, 5, 1, 1, 1, 13, 1, 9, 1, 5, 1, 1, 1, 13, 1, 9, 1, 5, 1, 1, 1,... = d(n).

Take d(n) by pairs: sums are 2, 2, 6, 2, 6, 2, 2, 10, 6, 2 = A167268.

Take d(n) by 2, 2, 4, 4, 6, 6, 8, 8, terms (in A052928): sums are 2, 2, 8, 8, 18, 18, 32, 32,... = extended A137583= 2, before A093907.

References

• Charles Janet, La classification hélicoidale des éléments chimiques, novembre 1928, Beauvais, 2+80 pages + 10 leaflets (see 3).

Links

• Charles Janet, Three-Dimensional Spiral-Tube System

Formula

A167268 = 2, 2, 6, 2, 6, 2, repeated = r(n) = 2, 2, 2, 2, 6, 6, 2, 2, 6, 6, 2, 2, 10, 10, 6, 6, 2, 2,...

a(n+2) - a(n) = r(n+1) = 2, 2, 2, 6, 6, 2, 2, n=1,2,3,...

a(2*n+1) - a(2*n) = 1 = A000012.