A168142 -id:A168142 - cp's OEIS frontend

A168234 A138100(n) + A168142(n).

3, 3, 13, 13, 13, 13, 13, 13, 13, 13, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 171, 171, 171, 171, 171, 171, 171

Offset: 1

Paul Curtz, Nov 21 2009

A138100 counts upwards in blocks of 2*k^2 numbers, restarting from 1,5,21,57,.. = A166464(k-1) = (2*k+1)*(2*k^2-4*k+3)/3, k>=1.
A168142 counts downwards in blocks of 2*k^2 numbers, restarting from 2*k^2, k>=1.
In consequence, the sequence here contains 2*k^2 copies of the number 1+2*k*(1+2*k^2)/3 = 1+A035597(k), k>=1,
where the sequence A035597 is a bisection of A168380.

Cf. A134984, A138725, A168208.

Edited by R. J. Mathar, Feb 15 2010

A171219 A138101(n)+A168142(n).

Original entry on oeis.org

5, 5, 21, 21, 21, 21, 21, 21, 21, 21, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121

Offset: 1

Paul Curtz, Dec 05 2009

This here basically repeats entries A168388(2k+1) 2*k^2 times for k=1,2,....

The construction is similar to A168234.

Comments tightened - R. J. Mathar, Nov 24 2010

A171710 Union of A168234 and A171219, sorted.

Original entry on oeis.org

3, 3, 5, 5, 13, 13, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89

Offset: 1

Paul Curtz, Dec 16 2009

Consider a table T(n,k) similar to A168142 = {2,1}, {8,7,6,...,2,1}, {18,17,...,2,1},... that repeats each row. Thus T(n,k) = {2,1}, {2,1}, {8,7,6,...,2,1}, {8,7,6,...,2,1}, {18,17,...,2,1}, etc. The rows of T(n,k) decrement from 2*ceiling(n/2)^2 to 1. Then we can construct the table of atomic numbers in the Janet periodic table A138509(n) = T(n,k) + a(n), with k=2*ceiling(n/2)^2 - 1 down to 1 by step -1.

Michael De Vlieger, Table of n, a(n) for n = 1..10680 (first 39 rows)

Cf. A138509 (Janet periodic table, rows n > 1 end in the repeated numbers in this sequence), A168234 (odd rows), A168380 (repeated numbers k - 1), A171219 (even rows), A172002 (smallest values of rows n > 1 are the repeated numbers in this sequence).

Table[(n + 1) (3 + 2 n^2 + 4 n - 3 (-1)^n)/12 + 1, {n, 7}, {k, 2 Ceiling[n/2]^2}] // Flatten (* Michael De Vlieger, Jul 20 2016 *)

May be regarded as an irregular triangle read by rows, defined by T(n,k) = A168380(n) + 1, with 1 <= k <= ceiling(n/2)^2. - Michael De Vlieger, Jul 20 2016

A168342 Even atomic numbers in the Janet table of the PSE, read right to left along rows.

Original entry on oeis.org

2, 4, 12, 10, 8, 6, 20, 18, 16, 14, 38, 36, 34, 32, 30, 28, 26, 24, 22, 56, 54, 52, 50, 48, 46, 44, 42, 40, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 120, 118, 116, 114, 112, 110, 108, 106, 104, 102, 100, 98, 96, 94, 92, 90

Offset: 1

Paul Curtz, Nov 23 2009

In the Janet arrangement, the elements appear in groups of twice 2, twice 8,... twice 2*k^2, and are here right-aligned:
...............................1,.2;
...............................3,.4;
.............5,.6,.7,.8,.9,10,11,12;
............13,14,15,16,17,18,19,20;
...28,39.30,31,32,33,34,35,36,37,38;
The even numbers in the table are read top-down, right-to-left and entered into the sequence (which, in consequence, is a permutation of the even numbers.)

			Skipping each second (i.e., each odd) element in the table, the result is
2;
4;
12,10,8,6;
20,18,16,14;
38,36,34,32,30,28,..
counting down the even numbers restarting at indices provided by A168380.

A. Tarantola, Periodic table of elements (Janet form)

Cf. A138100, A138101, A168142.

cp's OEIS Frontend

A168234 A138100(n) + A168142(n).

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A171219 A138101(n)+A168142(n).

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A171710 Union of A168234 and A171219, sorted.

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A168342 Even atomic numbers in the Janet table of the PSE, read right to left along rows.

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