A365440 Square array read by upward antidiagonals: T(n,k) is the n-th number j with the property that the parts of the symmetric representation of sigma(j) are two s-gon of width 1, where s = 2^(k+1), n >= 1, k >= 1.

3, 5, 10, 7, 14, 44, 11, 22, 52, 136, 13, 26, 68, 152, 592, 17, 34, 76, 184, 656

Offset: 1

Author

Omar E. Pol, Sep 25 2023

Keywords

• nonn
• tabl
• more

Comments

For column k = 1, 2, 3, 4, 5, ... the number of sides of the mentioned s-gon are respectively 4, 8, 16, 32, 64, ...

Conjecture 1: column k gives the row numbers of the triangle A364639 where the rows are [1, A036563(k+1) zeros, -1, 1] or where the rows start with [1, A036563(k+1) zeros, -1, 1] and the remaining terms are zeros.

Conjecture 2: every column gives a subsequence of A246955.

Conjecture 3: the sequence is infinite.

Observation 1: at least the terms <= 199 in increasing order coincide with at least the first 82 terms of the intersection of A071561 and A365406.

Observation 2: in the Example section of A246955 there is an irregular triangle. It seems that the terms sorted of the triangle give the sequence A246955. At least the first r(k) terms in the column (k - 1) of the triangle coincide with the first r(k) terms of the column k of this square array, where r(k) are 19, 18, 16, 14, 7 for k = 1..5 respectively.

Observation 3: at least the first five terms of the row 1 coincide with the first five terms of A246956.

Examples

			The corner of the square array is as shown below:
   3, 10,  44, 136, 592, ...
   5, 14,  52, 152, 656, ...
   7, 22,  68, 184, 688, ...
  11, 26,  76, 232, 752, ...
  13, 34,  92, 248, 848, ...
  17, 38, 116, 296, 944, ...
  19, 46, 124, 328, 976, ...
  ...
		

Crossrefs

Column 1 gives A065091.

Column 2 gives A362866.

Cf. A008578, A036563, A161344, A161345, A161424, A161835, A163280, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239929, A241008, A245092, A246955, A246956, A262626, A364639, A365406.