login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A296491 Decimal expansion of ratio-sum for A294170; see Comments. 4
6, 3, 5, 8, 7, 1, 3, 0, 2, 6, 9, 8, 4, 2, 9, 9, 3, 5, 4, 5, 4, 1, 4, 7, 7, 9, 6, 8, 8, 9, 0, 6, 0, 5, 5, 0, 4, 3, 0, 2, 3, 3, 0, 8, 6, 8, 8, 9, 4, 5, 7, 0, 7, 3, 2, 5, 1, 6, 1, 3, 3, 3, 0, 1, 0, 1, 5, 5, 4, 3, 0, 8, 3, 2, 4, 6, 4, 3, 7, 3, 6, 8, 1, 7, 5, 9 (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 = A294170, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.

LINKS

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

EXAMPLE

6.358713026984299354541477968890605504302...

MATHEMATICA

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

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

j = 1; While[j < 16, 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}];  (* A294170 *)

g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]

Take[RealDigits[s, 10][[1]], 100]  (* A296491 *)

CROSSREFS

Cf. A001622, A294170, A296284, A296492.

Sequence in context: A294386 A217769 A296501 * A085653 A022462 A319894

Adjacent sequences:  A296488 A296489 A296490 * A296492 A296493 A296494

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 20 2017

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 April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)