A392097 a(n) is the smallest number k for which the symmetric representation of sigma for k, SRS(k), has n parts and each i-th part up to the diagonal is unimodal of width i.

1, 3, 15, 75, 1225, 1275, 2145, 43125

Offset

1,2

Comments

All numbers a(n), n >= 12, are larger than 5 * 10^6, and 5 * 10^6 < a(9) <= 11^4 * 13^4, a(10) = 991875 and a(11) = 2247225.

Links

Table of n, a(n) for n=1..8.

Example

a(3) = 15 = 3 * 5 with SRS(15) = { 8, 8, 8 } and width pattern 1 0 1 2 1 0 1.
a(5) = 1225 = 5^2 * 7^2 with SRS(1225) = { 613, 216, 109, 216, 613 } and width pattern 1 0 1 2 1 0 1 2 3 2 1 0 1 2 1 0 1.

Mathematica

(* Functions partsSRS[ ] and widthPattern[ ] are defined in A377654 *)
a392097[b_, c_] := Module[{list=Table[0, c], k, len, wP}, For[k=1, k<=b, k++, len=Length[partsSRS[k]]; wP=Select[SplitBy[widthPattern[k], #==0&], #[[1]]==1&];
If[AllTrue[Range[(len+Boole[OddQ[len]])/2], Max[wP[[#]]]==#&&Length[wP[[#]]]==2#-1&]&&list[[len]]==0, list[[len]]=k]];
list]
a392097[43125, 8]

Crossrefs

Cf. A003056, A237591, A237270, A237271, A237593, A249223, A249351, A377654.

Sequence in context: A294340 A059838 A079164 * A240941 A047015 A322186

Adjacent sequences: A392094 A392095 A392096 * A392098 A392099 A392100

Keyword

nonn,more

Author

Hartmut F. W. Hoft, Dec 30 2025

Status

approved