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

0,2

Links

Table of n, a(n) for n=0..69.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A003215.

Sequence in context: A280026 A323080 A194806 * A156261 A071823 A219642

Adjacent sequences: A229787 A229788 A229789 * A229791 A229792 A229793

Keyword

nonn,easy

Author

Edmund Algeo, Oct 07 2013

Status

approved