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A086593 Bisection of A086592, denominators of the left-hand half of Kepler's tree of fractions. 6
2, 3, 4, 5, 5, 7, 7, 8, 6, 9, 10, 11, 9, 12, 11, 13, 7, 11, 13, 14, 13, 17, 15, 18, 11, 16, 17, 19, 14, 19, 18, 21, 8, 13, 16, 17, 17, 22, 19, 23, 16, 23, 24, 27, 19, 26, 25, 29, 13, 20, 23, 25, 22, 29, 26, 31, 17, 25, 27, 30, 23, 31, 29, 34, 9, 15, 19, 20, 21, 27, 23, 28, 21, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also denominator of alternate fractions in Kepler's tree as shown in A294442. - N. J. A. Sloane, Nov 20 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2048 (computed from b-file of A020650 provided by T. D. Noe)

FORMULA

a(n) = A086592(2n-1) = A020650(4n-2).

a(n+1) = A071585(n) + A071766(n), n >= 0. - Yosu Yurramendi, Jun 30 2014

From Yosu Yurramendi, Jan 04 2016: (Start)

a(2^(m+1)+k+1) - a(2^m+k+1) = A071585(k),  m >= 0, 0 <= k < 2^m.

a(2^(m+2)-k) = a(2^(m+1)-k) + a(2^m-k),   m > 0, 0 <= k < 2^m-1.

(End)

a(2^n) = A000045(n+3). - Antti Karttunen, Jan 29 2016, based on above.

a(n) = A020651(4n-1), a(n+1) = A020651(4n+1), n > 0. - Yosu Yurramendi, May 08 2018

a(2^m+k) = A071585(2^(m+1)+k),  m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, May 16 2018

MATHEMATICA

(* b = A020650 *) b[1] = 1; b[2] = 2; b[3] = 1; b[n_] := b[n] = Switch[ Mod[n, 4], 0, b[n/2 + 1] + b[n/2], 1, b[(n - 1)/2 + 1], 2, b[(n - 2)/2 + 1] + b[(n - 2)/2], 3, b[(n - 3)/2]]; a[1] = 2; a[n_] := b[4 n - 4]; Array[a, 100] (* Jean-Fran├žois Alcover, Jan 22 2016, after Yosu Yurramendi's formula for A020650 *)

PROG

(R)

  maxlevel <- 15

d <- c(1, 2)

for(m in 0:maxlevel)

for(k in 1:2^m) {

   d[2^(m+1)    +k] <- d[k] + d[2^m+k]

   d[2^(m+1)+2^m+k] <- d[2^(m+1)+k]

}

a <- vector()

for(m in 0:maxlevel) for(k in 0:(2^m-1)) a[2^m+k] <- d[2^(m+1)+k]

  a[1:63]

# Yosu Yurramendi, May 16 2018

CROSSREFS

Cf. A000045, A020650, A020651, A071585, A071766, A086592, A294442.

Sequence in context: A265535 A094802 A075084 * A073757 A088468 A049448

Adjacent sequences:  A086590 A086591 A086592 * A086594 A086595 A086596

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 28 2003

STATUS

approved

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)