A259225 Smallest oblong number greater than or equal to n.

0, 2, 2, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72

Offset

0,2

Links

Table of n, a(n) for n=0..66.

Casey Douglas, The Next Square or Pronic, June 2012. [Wayback Machine copy]

Formula

Sum_{n>=1} 1/a(n)^2 = 4 - Pi^2/3. - Amiram Eldar, Aug 16 2022

Mathematica

f[n_] := n*(n + 1); g[n_] := (Sqrt[4*n + 1] - 1)/2; a[n_] := f[Ceiling[g[n]]]; Array[a, 100, 0] (* Amiram Eldar, Aug 16 2022 *)

Prog

(PARI) a(n) = my(k = 0); while(k*(k+1)<n, k++); k*(k+1);

Crossrefs

Cf. A002378 (oblong numbers), A048761 (similar, with square instead).

Sequence in context: A319865 A350657 A140219 * A300951 A077081 A084700

Adjacent sequences: A259222 A259223 A259224 * A259226 A259227 A259228

Keyword

nonn

Author

Michel Marcus, Jun 21 2015

Status

approved