0,3

This sequence can be also obtained by starting complementing n's binary expansion from the second most significant bit, continuing towards lsb-end until the first 0-bit is reached, which is the last bit to be complemented.

A. Karttunen, Table of n, a(n) for n = 0..2047

Index entries for sequences that are permutations of the natural numbers

29 = 11101 in binary. By complementing bits in (zero-based) positions 3, 2 and 1 we get 10011 in binary, which is 19 in decimal, thus a(29)=19.

(MIT Scheme:) (define (a153142 n) (if (< n 2) n (let loop ((maskbit (a072376 n)) (z n)) (cond ((zero? maskbit) z) ((zero? (modulo (floor->exact (/ n maskbit)) 2)) (+ z maskbit)) (else (loop (floor->exact (/ maskbit 2)) (- z maskbit)))))))

Inverse: A153141. a(n) = A059893(A153152(A059893(n))) = A059894(A153151(A059894(n))). Differs from A003188 for the first time at n=10, where a(10)=14 while A003188(10)=15. Cf. also A072376. Corresponds to A069768 in the group of Catalan bijections.

Sequence in context: A165199 A120231 A083362 this_sequence A154447 A003188 A154435

Adjacent sequences: A153139 A153140 A153141 this_sequence A153143 A153144 A153145

nonn,base

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 20 2008