A014710 The regular paper-folding (or dragon curve) sequence.

2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2

Offset

0,1

Links

Ivan Panchenko, Table of n, a(n) for n = 0..10000

G. Melançon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.

Index entries for sequences obtained by enumerating foldings

Formula

Set a=2, b=1, S(0)=a, S(n+1) = S(n)aF(S(n)), where F(x) reverses x and then interchanges a and b; sequence is limit S(infinity).

a(4*n) = 2, a(4*n+2) = 1, a(2*n+1) = a(n).

Mathematica

Nest[Append[#1, If[EvenQ[#2], 2 - BitAnd[1, #2/2], #1[[Ceiling[#2/2]]]]] & @@ {#, Length@ #} &, {2}, 105] (* Michael De Vlieger, Apr 08 2021 *)

Prog

(PARI) a(n)=if(n%2==0, 2-bitand(1, n\2), a(n\2) );
for(n=0, 122, print1(a(n), ", "))
(Python)
def A014710(n):
    s = bin(n+1)[2:]
    m = len(s)
    i = s[::-1].find('1')
    return 2-int(s[m-i-2]) if m-i-2 >= 0 else 2 # Chai Wah Wu, Apr 08 2021

Crossrefs

See A014577 for more references and more terms.

The following are all essentially the same sequence: A014577, A014707, A014709, A014710, A034947, A038189, A082410. - N. J. A. Sloane, Jul 27 2012

Sequence in context: A323018 A192064 A225182 * A055174 A096369 A332289

Adjacent sequences: A014707 A014708 A014709 * A014711 A014712 A014713

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved