A199502 - OEIS

%I #13 Mar 30 2012 18:52:06

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

%T 57,70,71,80,81,86,87,88,89,102,103,112,113,118,119,120,121,138,139,

%U 152,153,162,163,168,169,170,171,188,189,202,203,212,213,218,219,220,221

%N From Janet helicoidal classification of the periodic table.

%C In A199426, we saw how Janet discovered

%C                                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 57

%C a(n) is the last row.

%C 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).

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

%C 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.

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

%H Charles Janet, <a href="http://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=289">Three-Dimensional Spiral-Tube System</a>

%F 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,...

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

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

%K nonn

%O 1,2

%A _Paul Curtz_, Nov 07 2011