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.

Previous Showing 11-18 of 18 results.

A011734 A binary m-sequence: expansion of reciprocal of x^21 + x^2 + 1 (mod 2, shifted by 20 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^21-1 = 2097151-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • Mathematica
    Join[PadRight[{},20,0],(Mod[#,2]&/@CoefficientList[Series[1/(x^21+x^2+1),{x,0,60}],x])] (* Harvey P. Dale, Jun 01 2020 *)
  • PARI
    A=matrix(N=21,N,i,j, if(i>1, i==j+1, setsearch([2,N], j)>0))*Mod(1,2); a(n)=lift((A^(n-#A+1))[1,1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^20/(x^21 + x^2 + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011735 A binary m-sequence: expansion of reciprocal of x^22 + x + 1 (mod 2, shifted by 21 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^22-1 = 4194303-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(N=22,N, i, j, if(i>1, i==j+1, setsearch([1,N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^21/(x^22 + x + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011736 A binary m-sequence: expansion of reciprocal of x^23 + x^5 + 1 (mod 2, shifted by 22 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^23-1 = 8388607-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(N=23,N,i,j, if(i>1, i==j+1, setsearch([5,N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^22/(x^23 + x^5 + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011737 A binary m-sequence: expansion of reciprocal of x^24 + x^4 + x^3 + x + 1 (mod 2, shifted by 23 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^24-1 = 16777215-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(N=24,N,i,j, if(i>1, i==j+1, setsearch([1,3,4,N],j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^23/(x^24 + x^4 + x^3 + x + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011739 A binary m-sequence: expansion of reciprocal of x^26 + x^8 + x^7 + x + 1 (mod 2, shifted by 25 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^26-1 = 67108863-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(N=26,N,i,j, if(i>1, i==j+1, setsearch([1,7,8,N],j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^25/(x^26 + x^8 + x^7 + x + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011740 A binary m-sequence: expansion of reciprocal of x^27 + x^8 + x^7 + x + 1 (mod 2, shifted by 26 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Sequence is 2^27-1 = 134217727-periodic. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(N=27,N,i,j, if(i>1, i==j+1, setsearch([1,7,8,N],j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ M. F. Hasler, Feb 17 2018

Formula

G.f. = x^26/(x^27 + x^8 + x^7 + x + 1) over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011741 A binary m-sequence: expansion of reciprocal of x^28 + x^3 + 1 (mod 2, shifted by 27 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Periodic with period of length 2^28 - 1. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • PARI
    A=matrix(28,28,i,j,if(i>1,i==j+1,setsearch([3,28],j)>0))*Mod(1,2); a(n)=lift((A^(n-27))[1,1]) \\ M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018

A011742 A binary m-sequence: expansion of reciprocal of x^29 + x^2 + 1 (mod 2, shifted by 28 initial 0's).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Periodic with period of length 2^29 - 1 = 536870911. - M. F. Hasler, Feb 17 2018

References

  • S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
  • H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
  • F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

  • Mathematica
    Join[PadRight[{},28,0],Mod[CoefficientList[Series[1/(x^29+x^2+1),{x,0,100}],x],2]] (* Harvey P. Dale, Sep 27 2024 *)
  • PARI
    A=matrix(29,29,i,j,if(i>1,i==j+1,setsearch([2,29],j)>0))*Mod(1,2); a(n)=lift((A^(n-28))[1,1]) \\ M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018
Previous Showing 11-18 of 18 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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