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A318843 a(n) is the smallest number k such that the symmetric representation of sigma(k) consists of n parts of width 1. 2
1, 3, 9, 21, 81, 147, 729, 903, 3025, 6875, 59049, 29095 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is infinite since, for example, for any n >= 1 the symmetric representation of sigma(3^n) consists of n + 1 parts of width 1. However, it is not increasing since a(11) = 59049 = 3^10 and a(12) = 29095 = 5 * 11 * 23^2. Also a(13) <= 531441 = 3^12.

This sequence is a subsequence of A174905; its subsequences a(n) for odd/even n are subsequences of A241010/A241008, respectively. Some even-indexed elements of this sequence are members of A239663, e.g., a(2), a(4), a(6), a(8) and a(12), but not a(10) = 6875.

The central pair of parts in the symmetric representation of sigma(a(2)), sigma(a(4)) and sigma(a(8)) meets at the diagonal (see A298856).

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

The smallest number k whose symmetric representation of sigma(k) consists of four parts of width one is a(4) = 21. The parts are 11, 5, 5, 11.

MATHEMATICA

(* Function path[] is defined in A237270 *)

segmentsSR[pathN0_, pathN1_] := SplitBy[Map[Min, Drop[Drop[pathN0, 1], -1] - pathN1], #==0&]

regions[pathN0_ , pathN1_] := Select[Map[Apply[Plus, #]&, segmentsSR[pathN0, pathN1]], #!=0&]

width1Q[pathN0_, pathN1_] := SubsetQ[{0, 1}, Union[Flatten[Drop[Drop[pathN0, 1], -1] - pathN1, 1]]]

(* parameter seq is the list of elements of the sequence in interval 1..m-1 already computed with an entry of 0 representing an element not yet found *)

a318843[m_, n_, seq_] := Module[{list=Join[seq, Table[0, 10]], path1=path[m-1], path0, k, a, r, w}, For[k=m, k<=n, k++, path0=path[k]; a=regions[path0, path1]; r=Length[a]; w=width1Q[path0, path1]; If[w && list[[r]]==0, list[[r]]=k]; path1=path0]; list]

a318843[2, 60000, {1}] (* data - actually computed in steps *)

CROSSREFS

Cf. A174905, A237270, A237593, A239663, A239665, A240062, A240542, A241008, A241010, A249351, A298856.

Sequence in context: A073947 A062811 A236856 * A001470 A118932 A053499

Adjacent sequences:  A318840 A318841 A318842 * A318844 A318845 A318846

KEYWORD

nonn,more

AUTHOR

Hartmut F. W. Hoft, Sep 04 2018

STATUS

approved

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Last modified July 4 18:38 EDT 2020. Contains 335448 sequences. (Running on oeis4.)