Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Feb 03 2020 15:25:46
%S 0,10,101,100,110,1001,1000,1010,1101,1100,1110,-1,-1,-1,-1,10001,
%T 10000,10010,10101,10100,10110,11001,11000,11010,11101,11100,11110,-1,
%U -1,-1,-1,100001,100000,100010,100101,100100,100110,101001,101000,101010,101101,101100,101110,-1,-1,-1,-1,110001
%N Binary string which equals n when 1's, 2's, 4's and 8's bits have weights -1, 1, 3, 6 respectively, while the other bits have their usual weights. -1 if no such string exists.
%C After a(10), the pattern seems to be sequences of sixteen a(n), four of which without solution, then 12 formed by placing a member of the binary sequence 1,10,11,11,100,101 etc. in front of re-occurring list of the same 12 4-digit numbers. The description does not lead to a unique sequence: a(0)=0 and a(0)=11 are both valid. a(3)=111 and a(3)=100 are both valid. - _R. J. Mathar_, Mar 14 2006
%D John M, Yarbough, Digital Logic Applications and Design, West Publishing, 1997. p. 25
%o (PARI) dig(n,digno,base) = { local(nshif) ; nshif=n ; for(shifr=0,digno-1, nshif = floor(nshif/base) ) ; nshif % base ; } binrep(n) = { local(nshif,resul) ; nshif=n; resul = Str(dig(nshif,0,2)) ; nshif=floor(nshif/2) ; while (nshif != 0, resul = concat(Str(dig(nshif,0,2)),resul) ; nshif=floor(nshif/2) ; ) ; return(resul) ; } modN(n) = { local(resul) ; resul = 16*floor(n/16) ; resul += -1*dig(n,0,2) ; resul += 1*dig(n,1,2) ; resul += 3*dig(n,2,2) ; resul += 6*dig(n,3,2) ; return(resul) ; } { for (n = 0, 60, for(an =0, 1000, if( modN(an) == n, anS = binrep(an) ; print1(anS,",") ; break ; ) ; if( an==1000, print("-1,") ); ) ; ) } - _R. J. Mathar_, Mar 14 2006
%Y Cf. A066335.
%K easy,sign
%O 0,2
%A _George E. Antoniou_, Dec 15 2001
%E More terms from _R. J. Mathar_, Mar 14 2006