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.

User: John McNamara

John McNamara's wiki page.

John McNamara has authored 3 sequences.

A066744 a(n) = either 4a(n-1)+1 or 4a(n-1)+3 depending on corresponding term of A005614, +3 for 0, +1 for 1.

Original entry on oeis.org

1, 7, 29, 117, 471, 1885, 7543, 30173, 120693, 482775, 1931101, 7724405, 30897623, 123590493, 494361975, 1977447901, 7909791605, 31639166423, 126556665693, 506226662775, 2024906651101, 8099626604405, 32398506417623
Offset: 1

Author

John McNamara, Jan 16 2002

Keywords

Comments

Ratio to terms of A028894 tends to 1.23459972586...

Crossrefs

Programs

  • Mathematica
    f[1]={0}; f[2]={1}; f[n_] := f[n]=Join[f[n-1], f[n-2]]; a[1]=1; a[n_] := a[n]=4a[n-1]+3-2f[9][[n]]; a/@Range[1, 30]

A066489 Binary expansion of n followed by its reverse complement.

Original entry on oeis.org

10, 1010, 1100, 100110, 101010, 110100, 111000, 10001110, 10010110, 10101010, 10110010, 11001100, 11010100, 11101000, 11110000, 1000011110, 1000101110, 1001010110, 1001100110, 1010011010, 1010101010, 1011010010, 1011100010, 1100011100, 1100101100, 1101010100
Offset: 1

Author

John McNamara, Jan 09 2002

Keywords

Examples

			a(2) = 1010 because 2 in binary is 10, the complement of which is 01, the reverse of which is 10, hence (10)(10). - _Sean A. Irvine_, Oct 22 2023
		

Crossrefs

Binary expansion of numbers in A035928.

Programs

  • Maple
    a:= n-> (l-> parse(cat(seq(l[-i], i=1..nops(l)), 1-~l[])))(Bits[Split](n)):
    seq(a(n), n=1..30);  # Alois P. Heinz, Oct 22 2023
  • PARI
    a(n)={my(v=binary(n)); fromdigits(concat(v,vector(#v,i,1-v[#v+1-i])))} \\ Andrew Howroyd, Oct 22 2023

Extensions

Title clarified and more terms from Sean A. Irvine, Oct 22 2023

A028894 a(n) = either 4a(n-1)+1 or 4a(n-1)+3 depending on corresponding term of A005614, +1 for 0, +3 for 1.

Original entry on oeis.org

1, 5, 23, 95, 381, 1527, 6109, 24439, 97759, 391037, 1564151, 6256607, 25026429, 100105719, 400422877, 1601691511, 6406766047, 25627064189, 102508256759, 410033027037, 1640132108151, 6560528432607, 26242113730429
Offset: 1

Author

John McNamara, Jan 12 2002

Keywords

Crossrefs

Programs

  • Mathematica
    f[1]={0}; f[2]={1}; f[n_] := f[n]=Join[f[n-1], f[n-2]]; a[1]=1; a[n_] := a[n]=4a[n-1]+1+2f[9][[n]]; a/@Range[1, 30]

Extensions

Edited by Dean Hickerson, Jan 14 2002