A034131 -id:A034131 - cp's OEIS frontend

A034121 Fractional part of cube root of a(n) starts with digit 5.

4, 16, 17, 43, 44, 45, 46, 92, 93, 94, 95, 96, 97, 167, 168, 169, 170, 171, 172, 173, 174, 175, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 615, 616, 617

Offset: 1

Patrick De Geest, Sep 15 1998

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A034131.

Select[Range[800],NumberDigit[CubeRoot[#],-1]==5&] (* Harvey P. Dale, Sep 06 2024 *)

A058034 Number of numbers whose cube root rounds to n.

Original entry on oeis.org

1, 3, 12, 27, 49, 75, 108, 147, 193, 243, 300, 363, 433, 507, 588, 675, 769, 867, 972, 1083, 1201, 1323, 1452, 1587, 1729, 1875, 2028, 2187, 2353, 2523, 2700, 2883, 3073, 3267, 3468, 3675, 3889, 4107, 4332, 4563, 4801, 5043, 5292, 5547, 5809, 6075, 6348

Offset: 0

Henry Bottomley, Nov 22 2000

			a(2)=12 since the cube roots of 4, 5, 6, ..., 15 all lie between 1.5 and 2.5.

Robert Israel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Cf. A003215 for number whose floor (or ceiling) of the cube root is n, A004277 for number whose square root rounds to n.

[n mod 4 eq 0 select 3*n^2+1 else 3*n^2: n in [0..80]]; // Vincenzo Librandi, Dec 25 2015

seq(1 + floor((n+1/2)^3) - ceil((n-1/2)^3), n = 0 .. 100);

Table[SeriesCoefficient[-(3 x^5 + 6 x^4 + 6 x^3 + 7 x^2 + x + 1)/((x - 1)^3 (x + 1) (x^2 + 1)), {x, 0, n}], {n, 0, 46}] (* Michael De Vlieger, Dec 24 2015 *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 3, 12, 27, 49, 75}, 50] (* Vincenzo Librandi, Dec 25 2015 *)

Vec(-(3*x^5+6*x^4+6*x^3+7*x^2+x+1)/((x-1)^3*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Jul 04 2014

a(n) = 3n^2+1 if n == 0 (mod 4), 3n^2 otherwise.
a(n) = A033428(n)+A011765(n) = A034131(n-1)-A034131(n-2).
a(n) = (1+(-1)^n+(-i)^n+i^n+12*n^2)/4 where i=sqrt(-1). - Colin Barker, Jul 04 2014
G.f.: -(3*x^5+6*x^4+6*x^3+7*x^2+x+1) / ((x-1)^3*(x+1)*(x^2+1)). - Colin Barker, Jul 04 2014

cp's OEIS Frontend

A034121 Fractional part of cube root of a(n) starts with digit 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A058034 Number of numbers whose cube root rounds to n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula