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A278765 Engel expansion of natural logarithm of golden ratio. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A179843 A243348 A136546 * A210881 A058729 A021303

Adjacent sequences:  A278762 A278763 A278764 * A278766 A278767 A278768

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 28 2016

STATUS

approved

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Last modified February 23 09:21 EST 2018. Contains 299503 sequences. (Running on oeis4.)