A229790 Cube roots of difference of consecutive cubes, rounded.

1, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24

Offset: 0

Author

Edmund Algeo, Oct 07 2013

Keywords

• nonn
• easy

Examples

			3n^2+3n+1 is the difference of two adjacent cubes, taking the cube root and rounding to a whole number yields an element of the series. 3 cubes is 27, inserting 3 into the formula = 37, 37 plus 27 is 64 the next cube after 27; the cube root of 37 is 3.33222... rounded to 3 is the element in the series.
		

Crossrefs

Cf. A003215.

Programs

Mathematica

Table[Round[(3*n^2 + 3*n + 1)^(1/3)], {n, 0, 100}] (* T. D. Noe, Oct 22 2013 *)
Round[Surd[#,3]]&/@Differences[Range[0,70]^3] (* Harvey P. Dale, Aug 01 2020 *)

PARI

a(n)=round((3*n*(n+1)+1)^(1/3)) \\ Charles R Greathouse IV, Oct 22 2013