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A066327
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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.
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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John M, Yarbough, Digital Logic Applications and Design, West Publishing, 1997. p. 25
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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