A392097 - OEIS

%I #9 Jan 11 2026 19:21:29

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

%N 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.

%C 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.

%e a(3) = 15 = 3 * 5 with SRS(15) = { 8, 8, 8 } and width pattern 1 0 1 2 1 0 1.

%e 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.

%t (* Functions partsSRS[ ] and widthPattern[ ] are defined in A377654 *)

%t 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&];

%t If[AllTrue[Range[(len+Boole[OddQ[len]])/2], Max[wP[[#]]]==#&&Length[wP[[#]]]==2#-1&]&&list[[len]]==0,list[[len]]=k]];

%t list]

%t a392097[43125, 8]

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

%K nonn,more

%O 1,2

%A _Hartmut F. W. Hoft_, Dec 30 2025