A368609 - OEIS

%I #7 Feb 04 2024 18:27:11

%S 0,2,4,0,8,10,2,14,16,0,6,20,8,2,26,28,4,12,34,14,6,38,40,2,18,44,10,

%T 4,50,0,12,24,56,58,26,2,64,8,16,68,70,32,4,10,0,76,36,80,6,38,22,86,

%U 14,24,42,8,94,98,4,100,0,48,104,106,30,110,6,12,20,54,2,56,34,22,14,124,36,128,4,62

%N a(n) = A368945(A071561(n)).

%C This sequence lists all nonnegative numbers in A368945, all of which are even.

%C Conjecture: Every nonnegative even number occurs in this sequence.

%e a(4) = A368945(A071561(4)) = A368945(10) = 0 and a(5) = A368945(A071561(5)) = A368945(11) = 8.

%e For numbers k <= 10^6 the largest width 0 extent instantiated is 999980 for prime 999983 and the smallest width 0 extent not instantiated by any k <= 10^6 is 31396.

%t a071561Q[n_] := Select[Divisors[n], Sqrt[n/2]<=#<Sqrt[2n]&]=={}

%t t249223[n_] := FoldList[#1+(-1)^(#2+1)KroneckerDelta[Mod[n-#2 (#2+1)/2, #2]]&, 1, Range[2, Floor[(Sqrt[8n+1]-1)/2]]] (* row n in triangle of A249223 *)

%t zeroExt[n_] := Module[{s=Position[t249223[n], 1][[-1, -1]]}, 2 Ceiling[(n+1)/(s+1)-(s+1)/2]-2]

%t a368609[n_] := Map[zeroExt, Select[Range[n], a071561Q]]

%t a368609[135]

%Y Cf. A071561, A071562, A235791, A237048, A237270, A237593, A249223, A368945.

%K nonn

%O 1,2

%A _Hartmut F. W. Hoft_, Jan 25 2024