A004074 a(n) = 2*A004001(n) - n, where A004001 is the Hofstadter-Conway $10000 sequence.

1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 1, 0, 1, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 7, 8, 7, 6, 7, 8, 7, 8, 7, 6, 7, 6, 5, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 11, 12, 11, 10, 11, 12, 13, 12, 13, 14, 13, 14, 13, 12

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The sequence is 0 at 2^n for n = 1, 2, 3, ... The maximum value between 2^n and 2^(n+1) appears to be A072100(n). - T. D. Noe, Jun 04 2012

Hofstadter shows the plot of sequence A004001(n)-(n/2) at point 10:52 of the part two of DIMACS lecture. This sequence is obtained by doubling those values, thus producing only integers. Cf. also A249071. - Antti Karttunen, Oct 22 2014

Links

• T. D. Noe (first 10000 terms) and Antti Karttunen, Table of n, a(n) for n = 1..16384
• D. R. Hofstadter, Analogies and Sequences: Intertwined Patterns of Integers and Patterns of Thought Processes, Lecture in DIMACS Conference on Challenges of Identifying Integer Sequences, Rutgers University, October 10 2014; Part 1, Part 2.
• T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
• Wikipedia, Blancmange curve
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A004001, A082590, A213057.

Cf. also A249071 (gives the even bisection halved), A233270 (also has a similar Blancmange curve appearance).

Programs

Mathematica

Clear[a]; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Table[2*a[n] - n, {n, 100}] (* T. D. Noe, Jun 04 2012 *)

Scheme

(define (A004074 n) (- (* 2 (A004001 n)) n)) ;; Other code as in A004001. - Antti Karttunen, Oct 22 2014

Formula

a(2^n)=0; for n >= 1, Sum_{i=2^(n-1)..2^n} a(i) = A082590(n-2). - Benoit Cloitre, Jun 04 2004

Extensions

More terms from Benoit Cloitre, Jun 04 2004