The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A301849 The Pagoda sequence: a sequence with isolated zeros in number-wall over finite fields. 3
 -1, 0, 1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, 0, -1, -1, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0, 1, 0, -1, -1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS c(0), c(1), ... is the fixed point of inflation morphism 1 -> 1 3, 2 -> 2 3, 3 -> 1 4, 4 -> 2 4, starting from state 1; a(-1), a(0), ... is the image of c(n) under encoding morphism 1 -> -1,-1,0,+1, 2 -> 0,-1,-1,+1, 3 -> 0,-1,+1,+1, 4 -> +1,-1,0,+1; where c(n) denotes A301848(n). The number-walls (signed Hankel determinants) over finite fields with characteristic -1 (mod 4) of this sequence have apparently only isolated zeros, though that has been proved only for p = 3,7. REFERENCES Jean-Paul Allouche and Jeffrey O. Shallit, Automatic sequences, Cambridge, 2003. LINKS W. F. Lunnon, The number-wall algorithm: an LFSR cookbook, Journal of Integer Sequences 4 (2001), no. 1, 01.1.1. Fred Lunnon, The Pagoda sequence: a ramble through linear complexity, number walls, D0L sequences, finite state automata, and aperiodic tilings, Electronic Proceedings in Theoretical Computer Science 1 (2009), 130-148. FORMULA a(n) = b(n+1) - b(n-1), where b(n) denotes A038189(n). MATHEMATICA b[n_] := b[n] = If[n == 0, 0, BitGet[n, IntegerExponent[n, 2] + 1]]; a[n_] := b[n+1] - b[n-1]; Array[a, 100, 0] (* Jean-François Alcover, Dec 13 2018 *) PROG (Magma) function b (n)   if n eq 0 then return 0; // alternatively,  return 1;   else while IsEven(n) do n := n div 2; end while; end if;   return n div 2 mod 2; end function; function a (n)   return b(n+1) - b(n-1); end function;   nlo := 0; nhi := 32;   [a(n) : n in [nlo..nhi] ]; CROSSREFS Cf. A038189, A301848, A301850. Sequence in context: A243566 A266112 A331990 * A074332 A152065 A267870 Adjacent sequences:  A301846 A301847 A301848 * A301850 A301851 A301852 KEYWORD sign AUTHOR Fred Lunnon, Mar 27 2018 EXTENSIONS More terms from Jean-François Alcover, Dec 13 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 15 02:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)