OFFSET
0,3
COMMENTS
a(n) = n iff n is a square or a pronic (or heteromecic) number of form k(k+1). The sequence interleaves individual squares with 2k copies of each pronic.
FORMULA
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/12 (A072691). - Amiram Eldar, Dec 04 2022
EXAMPLE
a(31) = 30 since 6 and 5 are on either side of the square root of 31 and 6*5 = 30.
MATHEMATICA
a[n_] := Ceiling[Sqrt[n]]*Floor[Sqrt[n]]; Array[a, 70, 0] (* Amiram Eldar, Dec 04 2022 *)
PROG
(Python)
from math import isqrt
def A038759(n): return m+n+k if (m:=(k:=isqrt(n))**2-n) else n # Chai Wah Wu, Jul 28 2022
(PARI) a(n) = my(r, s=sqrtint(n, &r)); if(r, n-r+s, n); \\ Kevin Ryde, Jul 30 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, May 03 2000
STATUS
approved