2,3

Also the number of zeros in the symmetric signed digit expansion of n with q=2 (i.e. the representation of n in the (-1,0,1)_2 number system). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 30 2003

Also the degree of the Stern polynomial B[n,t]. The Stern polynomials B[n,t] are defined by B[0,t]=0, B[1,t]=1, B[2n,t]=tB[n,t], B[2n+1,t]=B[n+1,t]+B[n,t] for n>=1 (see S. Klavzar et al. and A125184). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2006

C. Heuberger and H. Prodinger, On minimal expansions in redundant number systems: Algorithms and quantitative analysis, Computing 66(2001), 377-393.

S. Klavzar, U. Milutinovic and C. Petr, Stern polynomials, Adv. Appl. Math., (in press).

a(1)=0, a(2n)=a(n)+1, a(4n-1)=a(n)+1, a(4n+1)=a(n)+1 for n>=1 (Klavzar et al. Proposition 12). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2006

a(1)=0, a(2n)=a(n)+1, a(4n+1)=a(2n), a(4n+3)=a(2n+2) for n>=1 (Klavzar et al. Corollary 13). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2006

a(34)=4, which counts these reductions: 34->17->4->2->1.

a:=proc(n) if n=1 then 0 elif n mod 2=0 then a(n/2)+1 elif n mod 4=1 then a((n-1)/2) else a((n+1)/2) fi end: seq(a(n), n=2..91); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2006

ep(r, n)=local(t); t=n/2^(r+2):floor(t+5/6)-floor(t+4/6)-floor(t+2/6)+floor(t+1/6):for(n=1, 100, p=0:for(r=0, floor(log2(3*n))-1, if(ep(r, n)==0, p=p+1)): if(1, print1(p", ")))

Cf. A125184.

Sequence in context: A060501 A109129 A064122 this_sequence A033265 A096004 A071068

Adjacent sequences: A057523 A057524 A057525 this_sequence A057527 A057528 A057529

nonn

Clark Kimberling (ck6(AT)evansville.edu), Sep 03 2000