A390945 Burning number of the n-necklace graph.

2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Burning Number.

Eric Weisstein's World of Mathematics, Necklace Graph.

Formula

a(n) = A003059(3*n) = ceiling(sqrt(3*n)). - Andrew Howroyd, Feb 17 2026

Mathematica

Table[1 + Floor[Sqrt[3 n - 1]], {n, 20}]
Floor[Sqrt[3 Range[30] - 1]] + 1

Prog

(PARI) a(n) = 1 + sqrtint(3*n-1); \\ Andrew Howroyd, Feb 17 2026

Crossrefs

Cf. A003059.

Sequence in context: A132663 A306631 A023964 * A328179 A000267 A249728

Adjacent sequences: A390942 A390943 A390944 * A390946 A390947 A390948

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 17 2026

Extensions

a(16) onward from Andrew Howroyd, Feb 17 2026

Status

approved