cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A257853 a(n) = 2*n^3 - floor(2^(1/3)*n)^3.

Original entry on oeis.org

0, 1, 8, 27, 3, 34, 89, 174, 24, 127, 272, 465, 81, 298, 575, 918, 192, 565, 1016, 1551, 375, 946, 1613, 2382, 648, 1459, 2384, 62, 1029, 2122, 3347, 263, 1536, 2953, 4520, 566, 2187, 3970, 5921, 989, 3000, 5191, 7568, 1550, 3993, 6634, 9479, 2267, 5184, 8317
Offset: 0

Views

Author

M. F. Hasler, May 28 2015

Keywords

Comments

Is there a simple expression for a nontrivial lower bound for a(n)?

Examples

			a(4) = 2*4^3 - floor(2^(1/3)*4)^3 = 2*64 - 5^3 = 3.
a(5) = 2*5^3 - floor(2^(1/3)*5)^3 = 2*125 - 6^3 = 34.

Crossrefs

Cf. A087056 (analog for squares), A257854, A257855 (4th & 5th power).

Programs

  • Magma
    [2*n^3 - Floor(2^(1/3)*n)^3: n in [0..50]]; // Vincenzo Librandi, May 29 2015
  • Mathematica
    Table[2 n^3 - Floor[2^(1/3) n]^3, {n, 0, 60}] (* Vincenzo Librandi, May 29 2015 *)
  • PARI
    f(n,e=3,b=2)=n^e*b-floor(sqrtn(b,e)*n)^e

A257854 a(n) = 2*n^4 - floor(2^(1/4)*n)^4.

Original entry on oeis.org

0, 1, 16, 81, 256, 625, 191, 706, 1631, 3122, 5359, 721, 3056, 6497, 11296, 17729, 751, 7042, 15471, 26386, 40159, 57186, 11536, 28241, 48896, 73969, 103952, 14306, 43391, 78226, 119375, 167426, 12016, 58401, 112672, 175489, 247536, 226, 69647, 149426, 240319
Offset: 0

Views

Author

M. F. Hasler, May 28 2015

Keywords

Comments

Is there a simple expression for a nontrivial lower bound for a(n)?

Examples

			a(5) = 2*5^4 - floor(2^(1/4)*5)^4 = 2*625 - 5^4 = 625.
a(6) = 2*6^4 - floor(2^(1/4)*6)^4 = 2*1296 - 7^4 = 191.

Crossrefs

Cf. A087056 (analog for squares), A257853 & A257855 (3rd & 5th power).

Programs

  • Magma
    [2*n^4 - Floor(2^(1/4)*n)^4: n in [0..50]]; // Vincenzo Librandi, May 29 2015
  • Mathematica
    Table[2 n^4 - Floor[2^(1/4) n]^4, {n, 0, 60}] (* Vincenzo Librandi, May 29 2015 *)
  • PARI
    f(n,e=4,b=2)=n^e*b-floor(sqrtn(b,e)*n)^e
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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