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

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

0,3

Comments

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

Links

Table of n, a(n) for n=0..40.

Example

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.

Mathematica

Table[2 n^4 - Floor[2^(1/4) n]^4, {n, 0, 60}] (* Vincenzo Librandi, May 29 2015 *)

Prog

(PARI) f(n, e=4, b=2)=n^e*b-floor(sqrtn(b, e)*n)^e
(Magma) [2*n^4 - Floor(2^(1/4)*n)^4: n in [0..50]]; // Vincenzo Librandi, May 29 2015

Crossrefs

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

Sequence in context: A217261 A277562 A217709 * A017672 A055013 A080150

Adjacent sequences: A257851 A257852 A257853 * A257855 A257856 A257857

Keyword

nonn,easy

Author

M. F. Hasler, May 28 2015

Status

approved