A240809 a(n) = n for 1 <= n <= 4; thereafter a(n) = a(n - a(n-2)) + a(n - a(n-4)).

1, 2, 3, 4, 6, 6, 5, 6, 7, 8, 10, 10, 9, 10, 12, 12, 12, 12, 10, 12, 17, 16, 15, 16, 14, 16, 19, 20, 20, 18, 20, 20, 18, 22, 24, 22, 19, 24, 24, 24, 28, 24, 22, 24, 27, 32, 26, 28, 31, 28, 26, 32, 35, 32, 32, 32, 30, 32, 39, 40, 36, 34, 35, 34, 38, 40, 40, 42, 40, 38, 40, 40, 36, 44, 48, 42, 48, 44, 40, 46, 46, 46, 41, 48, 48, 48, 56, 48, 46, 48, 51, 48

Offset: 1

Author

N. J. A. Sloane, Apr 15 2014, Apr 17 2014

Keywords

• nonn

Comments

Conjectured to be infinite.

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

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000
• 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; Part 1, Part 2.
• D. R. Hofstadter, Plot of first 100000 terms
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A240821.

Programs

Magma

I:=[1, 2, 3, 4]; [n le 4 select I[n] else Self(n-Self(n-2))+Self(n-Self(n-4)): n in [1..100]]; // Vincenzo Librandi, Apr 16 2014

Maple

# Q(r,s) with initial values 1,2,3,4,...
r:=2; s:=4;
a:=proc(n) option remember; global r,s;
if n <= s then n
else
    if (a(n-r) <= n) and (a(n-s) <= n) then
    a(n-a(n-r))+a(n-a(n-s));
    else lprint("died with n =",n); return (-1);
    fi;
fi; end;
[seq(a(n),n=1..100)];