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 A065981 Best approximation of the remainder in the zeta(4) series using the remainder in the zeta(3) series. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 3 19:50 EST 2024. Contains 370512 sequences. (Running on oeis4.)