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.

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A240820 a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; f(k) = f(k-f(k-3)) + f(k-f(k-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

Original entry on oeis.org

20, 71, 34, 0, 46, 34, 36, 39, 90, 0, 142, 70, 91, 94, 255, 2004, 306, 525, 259, 454, 304, 1866, 316, 198, 254, 297, 415, 3315, 348, 406, 397, 420, 903, 1226, 408, 589, 1294, 535, 490, 958, 1343, 477, 492, 915, 1378, 1723, 797, 1869, 745, 696, 863, 1070, 560
Offset: 3

Views

Author

N. J. A. Sloane, Apr 15 2014

Keywords

Comments

The term a(6) = 0 is only conjectural.

References

  • D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014.

Links

Crossrefs

See A240827 for the sequence for n=6.
See A240823 for another version.
A diagonal of the triangle in A240821.

Extensions

More terms from Lars Blomberg, Oct 24 2014

A304590 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2, a(6) = 3; a(n) = a(n-a(n-3)) + a(n-a(n-6)) for n > 6.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 4, 8, 11, 11, 12, 12, 12, 4, 3, 3, 13, 6, 7, 7, 9, 10, 14, 9, 9, 19, 12, 13, 14, 15, 16, 18, 15, 15, 22, 18, 19, 10, 18, 18, 23, 18, 18, 24, 24, 26, 23, 24, 30, 31, 24, 29, 25, 30, 28, 25, 27, 29, 30, 30, 33, 37, 33, 38, 35, 33, 29, 31, 36, 41, 36, 36, 42, 28, 36, 37, 53, 36, 37, 41, 48, 48, 33
Offset: 1

Views

Author

Altug Alkan, May 15 2018

Keywords

Links

Crossrefs

Cf. A005185, A063882, A087777, A240827.

Programs

  • GAP
    a:=[1,1,1,2,1,3];; for n in [7..100] do a[n]:=a[n-a[n-3]]+a[n-a[n-6]]; od; a; # Muniru A Asiru, May 19 2018
  • Maple
    f:= proc(n) option remember; procname(n-procname(n-3))+procname(n-procname(n-6)) end proc:
for i from 1 to 6 do f(i):= [1,1,1,2,1,3][i] od:
map(f, [$1..100]); # Robert Israel, May 16 2018
  • Mathematica
    Nest[Append[#2, #2[[#1 - #2[[-3]] ]] + #2[[#1 - #2[[-6]] ]] ] & @@ {Length@ # + 1, #} &, {1, 1, 1, 2, 1, 3}, 77] (* Michael De Vlieger, Jul 20 2018 *)
  • PARI
    q=vector(100); q[1]=q[2]=q[3]=q[5]=1;q[4]=2;q[6]=3; for(n=7, #q, q[n]=q[n-q[n-3]]+q[n-q[n-6]]); q

A304621 a(n) = 10 - n for 1 <= n <= 9. Thereafter a(n) = a(n-a(n-3)) + a(n-a(n-6)).

Original entry on oeis.org

9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 5, 7, 15, 8, 10, 12, 8, 7, 9, 14, 13, 24, 11, 13, 21, 17, 16, 9, 14, 16, 33, 17, 16, 30, 20, 28, 9, 20, 16, 42, 26, 25, 39, 20, 28, 9, 29, 25, 51, 29, 28, 48, 26, 31, 9, 32, 31, 60, 32, 28, 57, 32, 37, 9, 32, 34, 69, 56, 37, 66, 26, 40, 9, 32, 40, 78, 56, 40, 75, 38, 52, 9, 44, 37, 87, 50
Offset: 1

Views

Author

Altug Alkan, May 15 2018

Keywords

Links

Crossrefs

Cf. A005185, A240827, A244477.

Programs

  • Magma
    [n le 9 select 10-n else Self(n-Self(n-3))+Self(n-Self(n-6)): n in [1..80]]; // Vincenzo Librandi, May 20 2018
  • Maple
    f:= proc(n) option remember; procname(n-procname(n-3))+procname(n-procname(n-6)) end proc:
for i from 1 to 9 do f(i):= 10-i od:
map(f, [$1..100]); # Robert Israel, May 16 2018
  • Mathematica
    Nest[Append[#, #[[1 + Length@ # - #[[-3]] ]] + #[[1 + Length@ # - #[[-6]] ]] ] &, Range[9, 1, -1], 77] (* Michael De Vlieger, May 20 2018 *)
  • PARI
    q=vector(10^5); for(n=1, 9, q[n]=9-n+1);for(n=10, #q, q[n]=q[n-q[n-3]]+ q[n-q[n-6]]); q
Showing 1-3 of 3 results.

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

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