login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297012 Decimal expansion of ratio-sum for A297011; see Comments. 2
2, 5, 1, 8, 4, 3, 9, 3, 4, 6, 0, 1, 2, 6, 2, 3, 9, 0, 0, 8, 9, 6, 8, 3, 7, 6, 4, 1, 1, 9, 1, 5, 5, 0, 6, 9, 1, 0, 1, 6, 3, 9, 3, 9, 8, 8, 1, 8, 7, 7, 7, 0, 4, 7, 5, 8, 6, 1, 5, 9, 6, 2, 5, 0, 9, 1, 5, 1, 5, 0, 9, 0, 9, 6, 8, 6, 3, 8, 2, 8, 2, 8, 1, 9, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n-1) -> g. The ratio-sum for A is |a(1)/a(0) - g| + |a(2)/a(1) - g| + . . . , assuming that this series converges. For A = A297011, we have g = 1 + sqrt(2). See A296425-A296434 for related ratio-sums and A296452-A296461 for related limiting power-ratios.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

ratio-sum = 2.518439346012623900896837641191550691016...

MATHEMATICA

a[0] = 3; a[1] = 5; b[0] = 1; b[1] = 2; b[2] = 4;

a[n_] := a[n] = 2 a[n - 1] + a[n - 2] - b[n];

j = 1; While[j < 9, k = a[j] - j - 1;

While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++];

u = Table[a[n], {n, 0, k}]; (* A297011 *)

r = 1 + Sqrt[2]; s = N[Sum[r - a[n]/a[n - 1], {n, 1, 1000}], 200];

StringJoin[StringTake[ToString[s], 41], "..."]

Take[RealDigits[s, 10][[1]], 100] (* A297012 *)

CROSSREFS

Cf. A297011.

Sequence in context: A124576 A283556 A268980 * A259449 A174815 A021401

Adjacent sequences:  A297009 A297010 A297011 * A297013 A297014 A297015

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Jan 13 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)