A193714 Positions of squares (A000290) in the union of squares and triangular numbers (A005214).

1, 3, 5, 8, 10, 12, 14, 16, 19, 21, 24, 26, 28, 31, 33, 36, 38, 40, 43, 45, 48, 50, 53, 55, 57, 60, 62, 65, 67, 69, 72, 74, 77, 79, 81, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 109, 112, 114, 117, 119, 122, 124, 126, 129, 131, 134, 136, 138, 141, 143

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A010052(A005214(a(n))) = 1.

a(n) ~ c * n, where c = 1 + sqrt(2) = A014176 = 2.414213... . - Amiram Eldar, Apr 04 2025

Mathematica

With[{max = 4000}, Position[Union[Join[Accumulate[Range[Floor[(Sqrt[8*max + 1] - 1)/2]]], Range[Floor[Sqrt[max]]]^2]], _?(IntegerQ[Sqrt[#]] &)] // Flatten] (* Amiram Eldar, Apr 04 2025 *)

Prog

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a193714 n = a193714_list !! (n-1)
a193714_list =
   map ((+ 1) . fromJust . (`elemIndex` a005214_list)) $ tail a000290_list

Crossrefs

Cf. A000290, A005214, A010052, A014176, A193715.

Sequence in context: A138829 A003265 A360394 * A184584 A342871 A191160

Adjacent sequences: A193711 A193712 A193713 * A193715 A193716 A193717

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2011

Status

approved