A066327 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.

0, 10, 101, 100, 110, 1001, 1000, 1010, 1101, 1100, 1110, -1, -1, -1, -1, 10001, 10000, 10010, 10101, 10100, 10110, 11001, 11000, 11010, 11101, 11100, 11110, -1, -1, -1, -1, 100001, 100000, 100010, 100101, 100100, 100110, 101001, 101000, 101010, 101101, 101100, 101110, -1, -1, -1, -1, 110001

Offset: 0

Author

George E. Antoniou, Dec 15 2001

Keywords

• easy
• sign

Comments

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

References

• John M, Yarbough, Digital Logic Applications and Design, West Publishing, 1997. p. 25

Crossrefs

Cf. A066335.

Programs

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

Extensions

More terms from R. J. Mathar, Mar 14 2006