

A060997


Decimal representation of continued fraction 1, 2, 3, 4, 5, 6, 7, ...


22



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

1,2


COMMENTS

The value of this continued fraction is the ratio of two Bessel functions: BesselI(0,2)/BesselI(1,2) = A070910/A096789. Or, equivalently, to the ratio of the sums: Sum_{n>=0} 1/(n!n!) and Sum_{n>=0} n/(n!n!).  Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003
1.43312...=[1,2,3,4,5,...] = shape of a rectangle which partitions into n squares at stage n; i.e. this is an example of the match between the continued fraction of a number r and a rectangle having shape r. See A188640.  Clark Kimberling, Apr 09 2011


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 70th [Birthday] Meeting, 2015, revised May 2016.
J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]


FORMULA

1/A052119.


EXAMPLE

1.433127426722311758317183455775...


MAPLE

A060997:=proc(q) local a, n; a:=n+1;
for n from q by 1 to 1 do a:=1/a+n; od; print(evalf(a, 100)); end:
A060997(10^5); # Paolo P. Lava, Mar 28 2013


MATHEMATICA

RealDigits[ FromContinuedFraction[ Range[ 44]], 10, 110] [[1]]
(* Or *) RealDigits[ BesselI[0, 2] / BesselI[1, 2], 10, 110] [[1]]
(* Or *) RealDigits[ Sum[1/(n!n!), {n, 0, Infinity}] / Sum[n/(n!n!), {n, 0, Infinity}], 10, 110] [[1]]


PROG

(PARI) besseli(0, 2)/besseli(1, 2) \\ Charles R Greathouse IV, Feb 19 2014


CROSSREFS

Cf. A052119, A001053.
Sequence in context: A177158 A177034 A177933 * A177270 A177160 A129624
Adjacent sequences: A060994 A060995 A060996 * A060998 A060999 A061000


KEYWORD

cons,easy,nonn


AUTHOR

Robert G. Wilson v, May 14 2001


STATUS

approved



