A386969 A variant of Recamán's sequence (A005132): a(0) = 0; for n > 0, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n + 3.

0, 4, 2, 8, 15, 10, 19, 12, 23, 14, 27, 16, 31, 18, 35, 20, 39, 22, 43, 24, 47, 26, 51, 28, 55, 30, 59, 32, 63, 34, 67, 36, 71, 38, 75, 40, 79, 42, 83, 44, 87, 46, 91, 48, 95, 50, 99, 52, 103, 54, 107, 56, 111, 58, 115, 60, 119, 62, 123, 64, 127, 66, 131, 68, 135, 70, 139, 72, 143, 74, 147, 76, 151

Offset

0,2

Comments

When visualized in connecting semicircular lines after a(n) = 8 it produces one increasingly large conical spiral.

Links

Zhuorui He, Table of n, a(n) for n = 0..1000

Formula

Conjectured g.f.: x*(4+2*x+11*x^3-2*x^4-9*x^5)/(1-x^2)^2. - Zhuorui He, Oct 20 2025

Conjectures from Bill McEachen, Jun 11 2026: (Start)

a(n) = n + 5 for odd n>2, a(n) = 2*n + 7 for even n for n>3.

a(n) = (3+(-1)^n)/2 * n + 6 + (-1)^n, n>2. (End)

Mathematica

a[n_] := a[n] = If[a[n-1] >= n && FreeQ[Table[a[k], {k, 0, n-1}], a[n-1] - n], a[n-1] - n, a[n-1] + n + 3]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Aug 22 2025 *)

Crossrefs

Cf. A005132, A386947.

Sequence in context: A225872 A231777 A288181 * A110622 A130078 A230900

Adjacent sequences: A386966 A386967 A386968 * A386970 A386971 A386972

Keyword

nonn

Author

Jules Beauchamp, Aug 11 2025

Status

approved