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 A296469 Decimal expansion of ratio-sum for A295862; see Comments. 44
 3, 8, 7, 0, 2, 3, 6, 0, 7, 9, 7, 9, 5, 9, 5, 9, 3, 2, 3, 2, 8, 2, 0, 5, 2, 3, 1, 1, 7, 8, 3, 9, 9, 5, 0, 1, 3, 8, 5, 6, 7, 3, 9, 8, 3, 0, 0, 9, 7, 2, 3, 1, 9, 9, 4, 3, 0, 1, 0, 8, 7, 6, 5, 5, 9, 5, 8, 0, 5, 4, 5, 4, 0, 6, 7, 3, 8, 5, 3, 9, 0, 5, 8, 8, 6, 2 (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 = A295862, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See A296425-A296434 for related ratio-sums and A296452-A296461 for related limiting power-ratios.  Guide to more ratio-sums and limiting power-ratios: **** Sequence A    ratio-sum for A     limiting power-ratio for A A295862           A296469                 A296470 A295947           A296471                 A296472 A295948           A296473                 A296474 A295949           A296475                 A296476 A295950           A296477                 A296478 A295951           A296479                 A296480 A295952           A296481                 A296482 A295953           A296483                 A296848 A295960           A296485                 A296486 A293076           A296487                 A296488 A293358           A296489                 A296490 A294170           A296491                 A296492 A296555           A296493                 A296494 A294414           A296495                 A296496 A294541           A296497                 A296498 A294546           A296499                 A296500 A294552           A296501                 A296494 A296776           A298171                 A298172 A294553           A296503                 A296504 A296556           A296565                 A296566 A296557           A296567                 A296568 A296558           A296569                 A296570 LINKS EXAMPLE ratio-sum = 6.21032710946618494227967... 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]; 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}]; (* A295862 *) g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200] Take[RealDigits[s, 10][[1]], 100]  (* A296469 *) CROSSREFS Cf. A001622, A296284, A296470. Sequence in context: A306933 A316565 A011413 * A010629 A016671 A010472 Adjacent sequences:  A296466 A296467 A296468 * A296470 A296471 A296472 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Dec 18 2017 STATUS approved

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)