A096151 -id:A096151 - cp's OEIS frontend

A215975 The integers floor((1.1)^k(n))/floor((1.1)^n) arising in A069751, where k(n) = A069751(n).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 5, 2, 1, 9, 5, 3, 6, 9, 2, 2, 2, 9, 9, 9, 22680, 31, 2, 34, 3335, 31, 9, 10, 881, 9450, 9450, 7875, 3637, 3637, 34, 130, 199394, 10364, 25784652043917, 73, 28372148, 3000, 348729431334264344425340064330765473421034034140890, 21279111, 6774778, 31, 3157469, 595, 182493908282594631, 1400, 13928971534455392

Offset: 1

N. J. A. Sloane, Aug 29 2012

nonn

Created to provide a check on the calculations in A096151.

Cf. A069751.

kln2[n_] :=  Module[{k = n + 1, den = Floor[ (11/10)^n]}, While[ ! IntegerQ[Floor[(11/10)^k]/den], k++]; Floor[(11/10)^k]/den]; Array[kln2,70] (* Harvey P. Dale, Aug 29 2012 *)

A235861 Regular continued fraction expansion of square root of 4729494.

Original entry on oeis.org

2174, 1, 2, 1, 5, 2, 25, 3, 1, 1, 1, 1, 1, 1, 15, 1, 2, 16, 1, 2, 1, 1, 8, 6, 1, 21, 1, 1, 3, 1, 1, 1, 2, 2, 6, 1, 1, 5, 1, 17, 1, 1, 47, 3, 1, 1, 6, 1, 1, 3, 47, 1, 1, 17, 1, 5, 1, 1, 6, 2, 2, 1, 1, 1, 3, 1, 1, 21, 1, 6, 8, 1, 1, 2, 1, 16, 2, 1, 15, 1, 1, 1, 1, 1, 1, 3, 25, 2, 5, 1, 2, 1, 4348

Offset: 0

Carsten Elsner, Jan 16 2014

This continued fraction is needed to solve completely Archimedes' cattle problem.

See Mathematica program in A096151. - Robert G. Wilson v, Dec 06 2014

C. Elsner, On Error Sums for Square Roots of Positive Integers with Applications to Lucas and Pell Numbers, J. Int. Seq. 17 (2014) # 14.4.4
I. Vardi, Archimedes' cattle problem, Am. Math. Monthly 105 (1998), pp. 305-319.

Cf. A096151.

Maple
```
cfrac(sqrt(4729494),500,quotients);
```

ContinuedFraction@ Sqrt@ 4729494 // Flatten (* Robert G. Wilson v, Dec 06 2014 *)

default(realprecision, 100); contfrac(sqrt(4729494)) \\ Michel Marcus, Mar 12 2015

a(n+92) = a(n) for n>0.

cp's OEIS Frontend

A215975 The integers floor((1.1)^k(n))/floor((1.1)^n) arising in A069751, where k(n) = A069751(n).

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A235861 Regular continued fraction expansion of square root of 4729494.

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