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A166242 Sequence generated from A014577, the dragon curve. 4
1, 2, 4, 2, 4, 8, 4, 2, 4, 8, 16, 8, 4, 8, 4, 2, 4, 8, 16, 8, 16, 32, 16, 8, 4, 8, 16, 8, 4, 8, 4, 2, 4, 8, 16, 8, 16, 32, 16, 8, 16, 32, 64, 32, 16, 32, 16, 8, 4, 8, 16, 8, 16, 32, 16, 8, 4, 8, 16, 8, 4, 8, 4, 2, 4, 8, 16, 8, 16, 32, 16, 8, 16, 32, 64, 32, 16, 32, 16, 8, 16, 32, 64, 32, 64, 128, 64, 32, 16, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

Rows of A164281 tend to A166242. Subsets of the first 2^n terms can be parsed into a binomial frequency of powers of 2; for example, the first 16 terms has as frequency of (1, 4, 6, 4, 1): (one 1, four 2's, six 4's, four 8's, and one 16.).

LINKS

Antti Karttunen, Table of n, a(n) for n = -1..8191

Index entries for sequences related to binary expansion of n

FORMULA

Let a(-1) = 1, then a(n+1) = 2*a(n) if A014577(n+1) = 1. If A014577(n+1) = 0, then a(n+1) = (1/2)*a(n).

As a recursive string in subsets of 2^n terms, the next subset = twice each term of current string, reversed, and appended.

EXAMPLE

From the Dragon curve, A014577:

...1...1...0...1...1...0...0...1... generates A166242:

1..2...4...2...4...8...4...2...4... given A166242(-1)=1.

By recursion, given the first four terms: (1, 2, 4, 2); reverse, double, and append to (1, 2, 4, 2) getting (1, 2, 4, 2, 4, 8, 4, 2,...).

MATHEMATICA

FoldList[If[EvenQ[((#2 + 1)/2^IntegerExponent[#2 + 1, 2] - 1)/2], 2 #1, #1/2] &, 1, Range[0, 89]] (* Michael De Vlieger, Jul 29 2017, after Jean-Fran├žois Alcover at A014577 *)

PROG

(Scheme, with memoization-macro definec)

;; Because definec does not work well with offset -1, we define an offset-0 based version of recurrence:

(definec (A166242off0 n) (if (zero? n) 1 (* (expt 2 (- (* 2 (A014577 (- n 1))) 1)) (A166242off0 (- n 1)))))

;; which the offset -1 version will invoke:

(define (A166242 n) (A166242off0 (+ 1 n)))

(define (A014577 n) (- 1 (A000035 (/ (- (A000265 (+ 1 n)) 1) 2))))

;; Scheme-code for A000035 and A000265 given under respective entries.

;; Antti Karttunen, Jul 27 2017

CROSSREFS

Cf. A014577, A164281.

Sequence in context: A296141 A286536 A318768 * A143107 A051638 A286580

Adjacent sequences:  A166239 A166240 A166241 * A166243 A166244 A166245

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Oct 10 2009

EXTENSIONS

More terms from Antti Karttunen, Jul 27 2017

STATUS

approved

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Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)