A016646 -id:A016646

Search: a016646 -id:a016646

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A016451

Continued fraction for log(23).

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(PARI) { 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

CROSSREFS

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

KEYWORD

nonn,cofr

AUTHOR

N. J. A. Sloane

STATUS

approved

A016669

Decimal expansion of log(46).

+10
2

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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.

LINKS

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

FORMULA

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

EXAMPLE

3.828641396489095000223984953268372686517880449200690996119315386976386....

MATHEMATICA

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

PROG

(PARI) 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

CROSSREFS

Cf. A016474 (continued fraction).

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved

A067923

Engel expansion of log(23).

+10
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..31.

PROG

(PARI) \\ a(1)=1 and for n>1:

s=log(23); for(i=1, 30, s=s*ceil(1/s)-1; print1(ceil(1/s), ", "); );

CROSSREFS

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.

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 03 2002

STATUS

approved

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