A173592 -id:A173592 - cp's OEIS frontend

A160914 Extended s-block elements for Janet table.

1, 2, 3, 4, 11, 12, 19, 20, 37, 38, 55, 56, 87, 88, 119, 120, 169, 170, 219, 220, 291, 292, 363, 364, 461, 462, 559, 560, 687, 688, 815, 816, 977, 978, 1139, 1140, 1339, 1340, 1539, 1540, 1781, 1782, 2023, 2024, 2311, 2312, 2599, 2600, 2937, 2938, 3275, 3276

Offset: 1

Paul Curtz, Oct 15 2011

See A168342. Must be included in A167268. From right to left, first vertical is A168380 from 1 to 8. Second vertical is A168380-1. In (1) page 12, introducing elements 93 to 120, Janet says that there is a probable 8th row. For row 8, he proposes, like for row 7, 32 elements (89 to 120). Page 16 he presents 4 blocks: first has 2*8 elements, second: 6*6, third: 10*4, fourth: 14*2. Today, blocks are s,p,d,f for Mendeleyev-Moseley-Seaborg 118 elements periodic table. See (2), (3), A173592 and A138509. In 1927, only 88 on the first 92 elements were known; 41 (1937 discovered), 61 (1947), 85 (1940) and 87 (1939) were missing. Since 2010 (117 discovered) the first 118 elements are known. Janet predicted only 120 elements.

			The following is an s-block, 2*8=16 elements, i.e., a(n) written vertically, after p-block, 6*6, (A138469).
                          1   2
                          3   4
5   6   7   8   9   10   11  12
13  14  15  16  17  18   19  20
31  32  33  34  35  36   37  38
49  50  51  52  53  54   55  56
81  82  83  84  85  86   87  88
113 114 115 116 117 118  119 120

Charles JANET, La structure du Noyau de l'atome,considérée dans la Classification périodique, des éléments chimiques, 1927 (Novembre) N. 2 Beauvais, 67 pages, 3 leaflets.

Cf. A099955.

A271996 The crystallogen sequence (a(n) = A018227(n)-4).

Original entry on oeis.org

6, 14, 32, 50, 82, 114, 164, 214, 286, 358, 456, 554, 682, 810, 972, 1134, 1334, 1534, 1776, 2018, 2306, 2594, 2932, 3270, 3662, 4054, 4504, 4954, 5466, 5978, 6556, 7134, 7782, 8430, 9152, 9874, 10674, 11474, 12356, 13238, 14206, 15174, 16232, 17290, 18442

Offset: 2

Natan Arie Consigli, Jun 18 2016

Terms up to 114 are the atomic numbers of the elements of group 14 in the periodic table. Those elements are also called crystallogens.

Colin Barker, Table of n, a(n) for n = 2..1000
Wikipedia, Carbon group.
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Cf. A173592, A018227.

Table[(6*(-9+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12, {n, 2, 10}] (* or *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {6, 14, 32, 50, 82, 114}, 50] (* G. C. Greubel, Jun 23 2016 *)

Vec(2*x^2*(3+x-x^2-2*x^3+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jun 19 2016

From Colin Barker, Jun 19 2016: (Start)
a(n) = (6*(-9 + (-1)^n) + (25 + 3*(-1)^n)*n + 12*n^2 + 2*n^3)/12.
a(n) = (n^3 + 6*n^2 + 14*n - 24)/6 for n even.
a(n) = (n^3 + 6*n^2 + 11*n - 30)/6 for n odd.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>7.
G.f.: 2*x^2*(3 + x - x^2 - 2*x^3 + x^5) / ((1-x)^4*(1+x)^2).
(End)

A058318 Number of energy levels in atoms of the n-th element of the periodic table.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Labos Elemer, Dec 12 2000

Run lengths, i.e., how many elements have 1,2,3,4,5,6,7 energy levels, are 2,8,8,18,18,32,26 (see A137583).

			For n=79, element 79 (Gold) has a(79)=6 energy levels (which may have 2,8,18,32,18,1 electrons).

Y. Bentor, Chemical Elements.Com
M. Winter, WebElements Periodic Table.

Cf. A007656, A018227, A058317, A137583, A173592.

seq(i$[2, 8, 8, 18, 18, 32, 32][i], i=1..7); # Michel Lagneau, Apr 03 2024

a(n) = m for s(m-1) < n <= s(m) for m=1..7, where s(m) = A173592(m) and s(0) = 0. - Michel Lagneau, Apr 03 2024

a(106)-a(118) from Michel Lagneau, Apr 03 2024

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A160914 Extended s-block elements for Janet table.

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A271996 The crystallogen sequence (a(n) = A018227(n)-4).

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A058318 Number of energy levels in atoms of the n-th element of the periodic table.

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