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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A296479 Decimal expansion of ratio-sum for A295951; see Comments. 3
2, 5, 7, 1, 9, 7, 1, 3, 6, 9, 3, 0, 7, 5, 7, 8, 2, 4, 5, 3, 4, 0, 6, 7, 2, 4, 8, 9, 6, 7, 2, 0, 8, 7, 6, 5, 9, 8, 7, 6, 8, 8, 8, 2, 5, 4, 5, 3, 3, 3, 9, 6, 3, 8, 1, 9, 6, 8, 6, 9, 0, 7, 4, 2, 8, 4, 3, 0, 5, 5, 0, 2, 3, 7, 4, 6, 4, 3, 3, 1, 8, 4, 7, 3, 5, 0 (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 = A295951, 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

ratio-sum = 2.571971369307578245340672489672087659876...

MATHEMATICA

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

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

j = 1; While[j < 13, k = a[j] - j - 1;

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

Table[a[n], {n, 0, k}]; (* A295951 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A296479 *)

CROSSREFS

Cf. A001622, A295951, A296284, A296480.

Sequence in context: A181583 A010589 A024715 * A024709 A101245 A004576

Adjacent sequences:  A296476 A296477 A296478 * A296480 A296481 A296482

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Jan 05 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 December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)