A065981 Best approximation of the remainder in the zeta(4) series using the remainder in the zeta(3) series.

1, 4, 7, 11, 15, 19, 24, 29, 35, 41, 47, 53, 60, 67, 74, 81, 89, 97, 105, 113, 121, 130, 139, 148, 157, 166, 176, 185, 195, 205, 216, 226, 237, 247, 258, 269, 280, 292, 303, 315, 326, 338, 350, 363, 375, 387, 400, 413, 426, 439, 452, 465, 478, 492, 505, 519

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Formula

Sum_{i > a(n)+1} 1/i^3 < Sum_{i > n} 1/i^4 < Sum_{i > a(n)} 1/i^3.

Mathematica

s1[a_] := Sum[1/i^3, {i, a + 1, Infinity}]; s2[n_] := Sum[1/i^4, {i, n + 1, Infinity}]; a[n_] := Module[{a = 1}, While[Not[s1[a + 1] < s2[n] < s1[a]], a++ ]; a]; Table[a[n], {n, 1, 20}] (* Jean-Francois Sadoc (sadoc(AT)lps.u-psud.fr), Feb 22 2007 *)

Crossrefs

Cf. A002117, A013662, A046092.

Sequence in context: A310737 A278452 A056548 * A244240 A310738 A310739

Adjacent sequences: A065978 A065979 A065980 * A065982 A065983 A065984

Keyword

nonn

Author

Benoit Cloitre, Dec 09 2001

Extensions

More terms from Sean A. Irvine, Sep 24 2023

Status

approved