This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365440 #35 Dec 31 2023 00:02:20 %S A365440 3,5,10,7,14,44,11,22,52,136,13,26,68,152,592,17,34,76,184,656 %N 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. %C A365440 For column k = 1, 2, 3, 4, 5, ... the number of sides of the mentioned s-gon are respectively 4, 8, 16, 32, 64, ... %C A365440 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. %C A365440 Conjecture 2: every column gives a subsequence of A246955. %C A365440 Conjecture 3: the sequence is infinite. %C A365440 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. %C A365440 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. %C A365440 Observation 3: at least the first five terms of the row 1 coincide with the first five terms of A246956. %e A365440 The corner of the square array is as shown below: %e A365440 3, 10, 44, 136, 592, ... %e A365440 5, 14, 52, 152, 656, ... %e A365440 7, 22, 68, 184, 688, ... %e A365440 11, 26, 76, 232, 752, ... %e A365440 13, 34, 92, 248, 848, ... %e A365440 17, 38, 116, 296, 944, ... %e A365440 19, 46, 124, 328, 976, ... %e A365440 ... %Y A365440 Column 1 gives A065091. %Y A365440 Column 2 gives A362866. %Y A365440 Cf. A008578, A036563, A161344, A161345, A161424, A161835, A163280, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239929, A241008, A245092, A246955, A246956, A262626, A364639, A365406. %K A365440 nonn,tabl,more %O A365440 1,1 %A A365440 _Omar E. Pol_, Sep 25 2023