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A368609
a(n) = A368945(A071561(n)).
6
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, 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, 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
OFFSET
1,2
COMMENTS
This sequence lists all nonnegative numbers in A368945, all of which are even.
Conjecture: Every nonnegative even number occurs in this sequence.
EXAMPLE
a(4) = A368945(A071561(4)) = A368945(10) = 0 and a(5) = A368945(A071561(5)) = A368945(11) = 8.
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.
MATHEMATICA
a071561Q[n_] := Select[Divisors[n], Sqrt[n/2]<=#<Sqrt[2n]&]=={}
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 *)
zeroExt[n_] := Module[{s=Position[t249223[n], 1][[-1, -1]]}, 2 Ceiling[(n+1)/(s+1)-(s+1)/2]-2]
a368609[n_] := Map[zeroExt, Select[Range[n], a071561Q]]
a368609[135]
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Jan 25 2024
STATUS
approved