A368609 a(n) = A368945(A071561(n)).

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.

Links

Table of n, a(n) for n=1..80.

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]

Crossrefs

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

Sequence in context: A011166 A181274 A115341 * A101160 A077624 A103191

Adjacent sequences: A368606 A368607 A368608 * A368610 A368611 A368612

Keyword

nonn

Author

Hartmut F. W. Hoft, Jan 25 2024

Status

approved