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A298171 Decimal expansion of ratio-sum for A296776; see Comments. 3
5, 6, 1, 1, 5, 6, 2, 0, 5, 7, 6, 5, 6, 2, 2, 5, 4, 7, 7, 0, 3, 2, 4, 4, 3, 4, 5, 6, 0, 9, 2, 5, 7, 9, 4, 8, 0, 9, 8, 2, 7, 0, 9, 5, 8, 6, 5, 5, 5, 5, 7, 3, 7, 0, 6, 5, 0, 1, 9, 0, 5, 7, 3, 9, 5, 3, 5, 1, 0, 5, 4, 3, 3, 1, 7, 6, 6, 7, 6, 0, 2, 0, 1, 0, 5, 4 (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 = A298171, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296462 for related sequences.

LINKS

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

EXAMPLE

ratio-sum = 5.611562057656225477032443456092579480982...

MATHEMATICA

a[0] = 1; a[1] = 3; b[0] = 2; 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}];  (* A296776 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A298171 *)

CROSSREFS

Cf. A001622, A296462, A296776.

Sequence in context: A047774 A243108 A287610 * A046614 A080130 A188640

Adjacent sequences:  A298168 A298169 A298170 * A298172 A298173 A298174

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Feb 09 2018

STATUS

approved

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Last modified February 25 02:54 EST 2020. Contains 332217 sequences. (Running on oeis4.)