A240827 a(n) = n for 1<=n<=6; thereafter a(n) = a(n-a(n-3))+a(n-a(n-6)).

1, 2, 3, 4, 5, 6, 9, 9, 9, 7, 8, 9, 10, 11, 12, 15, 15, 15, 13, 14, 15, 18, 18, 18, 18, 18, 18, 14, 16, 18, 25, 26, 24, 23, 22, 24, 20, 24, 24, 29, 28, 30, 29, 29, 27, 30, 28, 30, 27, 33, 33, 36, 32, 33, 27, 36, 36, 43, 36, 36, 38, 36, 36, 33, 32, 36, 39, 50, 48, 45, 39, 42, 37, 40, 42, 49, 44, 48, 48, 53, 48, 47, 42, 48, 44, 53, 48, 57, 52, 60

Offset: 1

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn
• hear

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..50000
• 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.
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A240821.

Programs

Magma

I:=[1,2,3,4,5,6]; [n le 6 select I[n] else Self(n-Self(n-3))+Self(n-Self(n-6)): n in [1..100]]; // Vincenzo Librandi, Apr 16 2014

Maple

#Q(r,s) with initial values 1,2,3,4,...
r:=3; s:=6;
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;
t2:=[seq(a(n),n=1..100)];

Mathematica

{a[1]=1,a[2]=2,a[3]=3,a[4]=4,a[5]=5,a[6]=6,a[n_]:=a[n]=a[n-a[n-3]]+ a[n-a[n-6]]};Table[a[x],{x,100}] (* Harvey P. Dale, Nov 18 2021 *)