A171710 Union of A168234 and A171219, sorted.

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

1,1

Comments

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.

Links

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

Formula

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

Mathematica

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 *)

Crossrefs

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).

Sequence in context: A213029 A348843 A290208 * A288983 A289768 A161220

Adjacent sequences: A171707 A171708 A171709 * A171711 A171712 A171713

Keyword

nonn,tabf

Author

Paul Curtz, Dec 16 2009

Status

approved