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

1,2

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

Table of n, a(n) for n=1..61.

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.

Crossrefs

Sequence in context: A241213 A362931 A047596 * A089964 A210495 A179302

Adjacent sequences: A199499 A199500 A199501 * A199503 A199504 A199505

Keyword

nonn

Author

Paul Curtz, Nov 07 2011

Status

approved