A016646 -id:A016646 - cp's OEIS frontend

A016451 Continued fraction for log(23).

3, 7, 2, 1, 1, 1, 2, 3, 1, 1, 1, 4, 158, 3, 2, 5, 1, 6, 4, 2, 72, 1, 2, 1, 5, 14, 3, 1, 5, 2, 2, 1, 4, 8, 1, 1, 1, 4, 18, 1, 1, 2, 1, 4, 2, 1, 1, 1, 2, 3, 3, 26, 1, 3, 1, 22, 3, 5, 1, 2, 2, 2, 1, 29, 2, 1, 2, 1, 8, 9, 2, 1, 2, 8, 19, 1, 1, 1

Offset: 1

N. J. A. Sloane

			3.135494215929149690806752831... = 3 + 1/(7 + 1/(2 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, May 17 2009

Harry J. Smith, Table of n, a(n) for n = 1..20000

Cf. A016646 Decimal expansion. - Harry J. Smith, May 17 2009

ContinuedFraction[Log[23],120] (* Harvey P. Dale, Jun 23 2020 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(log(23)); for (n=1, 20000, write("b016451.txt", n, " ", x[n])); } \\ Harry J. Smith, May 17 2009

A016669 Decimal expansion of log(46).

Original entry on oeis.org

3, 8, 2, 8, 6, 4, 1, 3, 9, 6, 4, 8, 9, 0, 9, 5, 0, 0, 0, 2, 2, 3, 9, 8, 4, 9, 5, 3, 2, 6, 8, 3, 7, 2, 6, 8, 6, 5, 1, 7, 8, 8, 0, 4, 4, 9, 2, 0, 0, 6, 9, 0, 9, 9, 6, 1, 1, 9, 3, 1, 5, 3, 8, 6, 9, 7, 6, 3, 8, 6, 8, 6, 7, 9, 5, 4, 4, 9, 3, 0, 1, 3, 8, 0, 4, 2, 6, 4, 4, 1, 9, 1, 4, 9, 4, 1, 3, 5, 0

Offset: 1

N. J. A. Sloane

			3.828641396489095000223984953268372686517880449200690996119315386976386....

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

Harry J. Smith, Table of n, a(n) for n = 1..20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for transcendental numbers

Cf. A016474 (continued fraction).

RealDigits[Log[46], 10, 120][[1]] (* Vincenzo Librandi, Jun 21 2015 *)

default(realprecision, 20080); x=log(46); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016669.txt", n, " ", d)); \\ Harry J. Smith, May 21 2009

Equals A002162+A016646. - R. J. Mathar, Jun 07 2024

A067923 Engel expansion of log(23).

Original entry on oeis.org

1, 1, 1, 8, 12, 135, 199, 378, 600, 1836, 4897, 8198, 8993, 84887, 450287, 892157, 5053447, 5183243, 15350505, 19963471, 31631271, 37655416, 2138752269, 4805947342, 14508700588, 27508373127, 28635924075, 30814114095, 32073629885, 961160400603, 3607716972786

Offset: 1

Benoit Cloitre, Mar 03 2002

See A006784 for explanation of Engel expansions. Log(23) is the first number of the form Log(n), n an integer, for which it is not known whether a BBP formula exists.

Cf. A016646.

\\ a(1)=1 and for n>1:
s=log(23); for(i=1,30,s=s*ceil(1/s)-1; print1(ceil(1/s),","); );

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A016451 Continued fraction for log(23).

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A016669 Decimal expansion of log(46).

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A067923 Engel expansion of log(23).

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