A390405 Denominators of greedy Egyptian fraction for Apéry's constant, zeta(3).

1, 5, 487, 284490, 138804750010, 36614447980107265380005, 1488687402158277572727530663796523771436167916, 6851755410566409402388858507918754752119691856571335811091610144283832011776672133933360212

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Eric Weisstein's World of Mathematics, Egyptian Fraction.

Index entries for sequences related to Egyptian fractions

Formula

a(n) = ceiling(1/(zeta(3) - Sum_{i=0..n-1} 1/a(i))).

Example

a(3) = 487 since zeta(3) = 1.202056903..., 1/1 + 1/5 + 1/486 = 1.202057613... is larger, and 1/1 + 1/5 + 1/487 = 1.202053388... is smaller.

Crossrefs

Cf. A002117 (decimal expansion), A013631 (continued fraction), A053980, A059415, A059416, A059537, A084225, A084226, A088453, A152648.

Cf. A006487 (for sqrt(2)), A144835 (for 1/zeta(2)).

Sequence in context: A206502 A198249 A160363 * A268113 A308132 A352181

Adjacent sequences: A390402 A390403 A390404 * A390406 A390407 A390408

Keyword

nonn

Author

Michael B. Porter, Nov 04 2025

Extensions

More terms from Sean A. Irvine, Nov 12 2025

Status

approved