A199426 -id:A199426 - cp's OEIS frontend

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

Paul Curtz, Nov 07 2011

nonn

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.

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

Charles Janet, Three-Dimensional Spiral-Tube System

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.

cp's OEIS Frontend

A199502 From Janet helicoidal classification of the periodic table.

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