A249071 - OEIS

A249071

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

COMMENTS

Hofstadter shows the plot of function A004001(n)-(n/2) at time 10:52 during the part two of DIMACS lecture. This sequence is obtained as the bisection of that function, thus containing only integers. Cf. also A004074.

LINKS

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.

Wikipedia, Blancmange curve

Index entries for Hofstadter-type sequences

FORMULA

a(n) = A004001(2*n) - n.

a(n) = A004074(2*n) / 2. [Also the even bisection of A004074 halved.]

PROG

(Scheme, two alternative versions):

(define (A249071 n) (- (A004001 (* 2 n)) n))

(define (A249071 n) (/ (A004074 (* 2 n)) 2))

CROSSREFS

Cf. A004001, A004074.

Cf. also A233270 (also has a similar Blancmange curve appearance).