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 1-3 of 3 results.

A103379 a(n) = a(n-11) + a(n-12).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 64, 64, 64, 65, 71, 86, 106, 121, 127
Offset: 1

Views

Author

Jonathan Vos Post, Feb 15 2005

Keywords

Links

Crossrefs

Cf. A079398, A103372-A103378, A103380, A103389, A103399.

Programs

  • Maple
    A103379 := proc(n) option remember ; if n <= 12 then 1; else procname(n-11)+procname(n-12) ; fi; end: for n from 1 to 120 do printf("%d,",A103379(n)) ; od: # R. J. Mathar, Aug 30 2008
  • Mathematica
    SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Ray Chandler and Robert G. Wilson v *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1,1,1,1},100] (* Harvey P. Dale, Jan 31 2015 *)

Formula

For n>12: a(n) = a(n-11) + a(n-12). a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = a(11) = a(12) = 1.
G.f.: x*(1-x^11) / ((1-x)*(1-x^11-x^12)). - Colin Barker, Mar 26 2013

Extensions

Corrected from a(11) on by R. J. Mathar, Aug 30 2008

A103399 Semiprimes in A103379.

Original entry on oeis.org

4, 9, 15, 21, 33, 38, 58, 65, 86, 106, 121, 129, 265, 511, 2047, 2049, 4097, 4109, 17855, 19857, 32663, 34709, 104739, 130393, 131889, 140474, 220918, 262978, 266174, 274759, 540933, 568083, 1312526, 1665242, 1833203, 2179101, 2295571
Offset: 1

Views

Author

Jonathan Vos Post, Feb 15 2005

Keywords

Examples

			A103379(21) = 4 = 2 * 2, which is semiprime, hence 4 is in this sequence.

Crossrefs

Cf. A001358, A103379, A103389.

Programs

  • Maple
    isA103379 := proc(n)
    option remember ;
    local i ;
    for i from 1 do
        if A103379(i) = n then
            return true ;
        elif A103379(i) > n then
            return false ;
        fi;
    od:
end proc:
A103399 := proc(n)
    option remember ;
    local a, i ;
    if n = 1 then
        4;
    else
        for a from procname(n-1)+1 do
            if numtheory[bigomega](a) = 2 then
                if isA103379(a) then
                    return a ;
                fi;
            fi;
        end do:
    end if;
end proc:
for n from 1 do
    printf("%d,\n",A103399(n)) ;
end do: # R. J. Mathar, Aug 30 2008
  • Mathematica
    SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; Clear[a]; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by Ray Chandler and Robert G. Wilson v *)

Formula

Intersection of A103379 and A001358.

Extensions

Corrected from a(15) on by R. J. Mathar, Aug 30 2008

A103400 Semiprimes in A103380.

Original entry on oeis.org

4, 9, 15, 21, 33, 38, 58, 65, 86, 106, 121, 129, 265, 511, 2047, 2049, 4097, 4109, 8193, 17855, 19857, 34709, 66233, 104739, 130953, 131209, 140474, 220918, 258931, 511673, 540951
Offset: 1

Views

Author

Jonathan Vos Post, Feb 16 2005

Keywords

Crossrefs

Cf. A001358, A103380.

Programs

  • Maple
    A103380 := proc(n) option remember ; if n <= 13 then 1; else procname(n-12)+procname(n-13) ; fi; end: isA103380 := proc(n) option remember ; local i ; for i from 1 do if A103380(i) = n then RETURN(true) ; elif A103380(i) > n then RETURN(false) ; fi; od: end: A103400 := proc(n) option remember ; local a,i ; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then if isA103380(a) then RETURN(a) ; fi; fi; od: fi; end: for n from 1 to 37 do printf("%d, ",A103400(n)) ; od: # R. J. Mathar, Aug 30 2008
  • Mathematica
    SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; Clear[a]; k12; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by Ray Chandler and Robert G. Wilson v *)

Formula

Intersection of A103380 and A001358.

Extensions

Corrected from a(15) on by R. J. Mathar, Aug 30 2008
Showing 1-3 of 3 results.

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