A129602 In the binary expansion of n replace each run of k 0's (or 1's) with 2k-1 0's (or 1's), except in the most significant run where we double the number of 0's (or 1's).

0, 3, 6, 15, 24, 13, 30, 63, 96, 49, 26, 55, 120, 61, 126, 255, 384, 193, 98, 199, 104, 53, 110, 223, 480, 241, 122, 247, 504, 253, 510, 1023, 1536, 769, 386, 775, 392, 197, 398, 799, 416, 209, 106, 215, 440, 221, 446, 895, 1920, 961, 482, 967, 488, 245, 494

Offset

0,2

Links

Table of n, a(n) for n=0..54.

Example

a(1) = 3, as 1 is 1 in binary and doubling the number of 1's (in the only run) gives binary 11, 3 in decimal. a(9) = 49, as 9 is 1001 in binary and replacing the most significant run '1' with '11' and the center run '00' with '000' and the least significant run '1' with '1', we get 110001 in binary, 49 in decimal.

Prog

(MIT/GNU Scheme)
;;; binexp->runcount1list and runcount1list->binexp given in A129594.
(define (A129602 n) (if (zero? n) n (let ((rl (binexp->runcount1list n))) (runcount1list->binexp (cons (* 2 (car rl)) (map (lambda (i) (- (* 2 i) 1)) (cdr rl)))))))

Crossrefs

Central diagonal of array A129600, a(n) = A129600bi(n, n). Cf. A129594. For n > 0, a(n) = A004760(A129603(n)+1).

Sequence in context: A253651 A180322 A244164 * A044888 A179805 A006639

Adjacent sequences: A129599 A129600 A129601 * A129603 A129604 A129605

Keyword

nonn,base

Author

Antti Karttunen, May 01 2007

Extensions

Edited definition. - N. J. A. Sloane, Dec 20 2023

Status

approved