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

1,6

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

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

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 *)

Prog

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

Crossrefs

Cf. A004001, A082590, A213057.

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

Sequence in context: A348295 A362598 A179765 * A245615 A053646 A080776

Adjacent sequences: A004071 A004072 A004073 * A004075 A004076 A004077

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Benoit Cloitre, Jun 04 2004

Status

approved