cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A120634 Decimal equivalent of A066335.

Original entry on oeis.org

0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28, 35, 34, 33, 32, 39, 38, 37, 36, 43, 42, 41, 40, 47, 46, 45, 44, 51, 50, 49, 48, 55, 54, 53, 52, 59, 58, 57, 56, 63, 62, 61, 60, 67, 66, 65, 64, 71, 70, 69, 68, 75, 74, 73
Offset: 0

Views

Author

Joshua Zucker, Jun 21 2006

Keywords

Comments

The same as A004444 except for first 3 terms. - Pietro Battiston, Jan 19 2008

Links

Crossrefs

Cf. A004444, A066335.

Programs

  • Mathematica
    LinearRecurrence[{1,0,0,1,-1},{0,7,6,5,4},80] (* Harvey P. Dale, May 10 2015 *)
  • PARI
    concat(0, Vec(-x*(x^3+x^2+x-7)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100))) \\ Colin Barker, Oct 06 2014

Formula

From Colin Barker, Oct 06 2014: (Start)
a(n) = (3-(-1)^n-(1-i)*((-i)^n+i*i^n)+n) where i=sqrt(-1).
a(n) = a(n-1)+a(n-4)-a(n-5).
G.f.: -x*(x^3+x^2+x-7) / ((x-1)^2*(x+1)*(x^2+1)).
(End)

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.

Original entry on oeis.org

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

Views

Author

George E. Antoniou, Dec 15 2001

Keywords

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

A066329 Binary string which equals n when 1's, 2's, 4's and 8's bits have weights 1, 1, 3, 5 respectively, while the other bits have their usual weights. -1 if no such string exists.

Original entry on oeis.org

0, 1, 11, 100, 101, 1000, 1001, 1011, 1100, 1101, 1111, -1, -1, -1, -1, -1, 10000, 10001, 10011, 10100, 10101, 11000, 11001, 11011, 11100, 11101, 11111, -1, -1, -1, -1, -1, 100000, 100001, 100011, 100100, 100101, 101000, 101001, 101011, 101100, 101101, 101111, -1, -1, -1, -1, -1, 110000, 110001, 110011
Offset: 0

Views

Author

George E. Antoniou, Dec 15 2001

Keywords

References

  • John M. Yarbrough, Digital Logic Applications and Design, West Publishing, 1997, p. 26

Crossrefs

Cf. A066335.
A120631 is the decimal conversion of these binary strings.

Extensions

More terms from Joshua Zucker, Jun 21 2006

A066330 Binary string which equals n when 1's, 2's, 4's and 8's bits have weights 1, 2, 4, 5 respectively, while the other bits have their usual weights. -1 if no such string exists.

Original entry on oeis.org

0, 1, 10, 11, 100, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, -1, -1, -1, 10000, 10001, 10010, 10011, 10100, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, -1, -1, -1, 100000, 100001, 100010, 100011, 100100, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 101111, -1, -1, -1
Offset: 0

Views

Author

George E. Antoniou, Dec 15 2001

Keywords

Comments

There are engineering reasons for this encoding, but it is unsatisfactory from a mathematical point of view since 5 could equally well be 101.

References

  • John M. Yarbrough, Digital Logic Applications and Design, West Publishing, 1997, p. 26

Crossrefs

Cf. A066335, A066338.

Extensions

More terms from Joshua Zucker, Jun 21 2006

A066334 Binary string which equals n when 1's, 2's, 4's and 8's bits have weights 1, 2, 4, 2 respectively, while the other bits have their usual weights. -1 if no such string exists.

Original entry on oeis.org

0, 1, 10, 11, 100, 101, 110, 111, 1110, 1111, -1, -1, -1, -1, -1, -1, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11110, 11111, -1, -1, -1, -1, -1, -1, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 101110, 101111, -1, -1, -1, -1, -1, -1, 110000, 110001, 110010, 110011
Offset: 0

Views

Author

George E. Antoniou, Dec 15 2001

Keywords

References

  • Morris M. Mano, Digital Design, Prentice Hall, 2002. p. 20.

Crossrefs

Cf. A066335.

Extensions

More terms from Joshua Zucker, Jun 21 2006
Showing 1-5 of 5 results.

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