A278765 Engel expansion of natural logarithm of golden ratio.

3, 3, 4, 4, 4, 6, 15, 48, 118, 147, 671, 1026, 3075, 44641, 48364, 1868380, 75080506, 96848501, 911582093, 2511879981, 8700005050, 15888441652, 108526838262, 446779835336, 632466801279, 1084794852728, 1184722346307, 1657692322844, 12376968750845, 17341469111712, 27996895637798, 38935285631573

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Engel Expansion

Eric Weisstein's World of Mathematics, Golden Ratio

Index entries for sequences related to Engel expansions

Example

log(phi)  = 0.4812118250596... = 1/3 + 1/(3*3) + 1/(3*3*4) + 1/(3*3*4*4) + 1/(3*3*4*4*4) + 1/(3*3*4*4*4*6) + ...

Mathematica

EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[Log[GoldenRatio], 7! ], 40]

Crossrefs

Cf. A006784 (for definition of Engel expansion).

Cf. A001622, A002390, A028259, A059195.

Sequence in context: A319198 A243348 A136546 * A210881 A058729 A021303

Adjacent sequences: A278762 A278763 A278764 * A278766 A278767 A278768

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 28 2016

Status

approved