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A218252 Start with 1. For each term m, the next term is the smallest positive integer k such that k - (sum of base 2 digits of k) = m. If no such k exists, use the smallest natural number not already in the sequence. 5
1, 2, 3, 4, 6, 5, 7, 8, 10, 12, 9, 11, 14, 13, 15, 16, 18, 20, 17, 19, 22, 24, 21, 23, 26, 30, 25, 28, 27, 29, 31, 32, 34, 36, 33, 35, 38, 40, 37, 39, 42, 46, 48, 41, 44, 43, 45, 47, 50, 54, 58, 49, 52, 51, 53, 56, 60, 55, 57, 62, 59, 61, 63, 64, 66, 68, 65, 67, 70, 72, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is a permutation of the positive integers.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

To obtain the 2nd term, take the first, 1.  What is the smallest integer k so that k - the number of 1's in k's binary representation is 1? The answer, obviously, is 2. [A213723(1) = 2.]

There is no number that is 2 more than its binary weight [as A213723(2) = 0], therefore we just take 3 as the next term.

Following 3 we can choose either 4 or 5, but 4 is smaller, and is thus the next term of the sequence. [A213723(3) = 4.]

PROG

(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)

(defineperm1 (A218252 n) (cond ((<= n 1) n) ((A213723 (A218252 (- n 1))) => (lambda (next_maybe) (if (not (zero? next_maybe)) next_maybe (let loop ((i (A000012 (- n 1)))) (if (not-lte? (A257683 i) n) i (loop (+ i 1)))))))))

;; We consider a > b (i.e. not less than b) also in case a is nil.

;; (Because of the stateful caching system used by defineperm1-macro):

(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

;; Antti Karttunen, May 04 2015

CROSSREFS

Inverse permutation: A257683.

Cf. A000120, A005187, A011371, A213723, A218253, A218254.

Cf. also A257676.

Sequence in context: A332807 A267106 A275119 * A080541 A330081 A072759

Adjacent sequences:  A218249 A218250 A218251 * A218253 A218254 A218255

KEYWORD

nonn

AUTHOR

Nico Brown, Oct 24 2012

EXTENSIONS

Name slightly edited and links to A213723 in examples added by Antti Karttunen, May 04 2015

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)