0,3

To make this a permutation of nonnegative integers, we subtract one from each run count except for the most significant run, e.g. a(11) = 9, as 11 = 1011 and 9+1 = 10 = 5^1 * 3^(1-1) * 2^(2-1).

Index entries for sequences that are permutations of the natural numbers

(MIT Scheme with Aubrey Jaffer's SLIB library:)

(require 'factor)

(define (A075157 n) (-1+ (binruns->primefactorization n)))

(define (binruns->primefactorization n) (let loop ((n n) (i 0) (p (modulo (1+ n) 2)) (z 1)) (cond ((zero? n) (* z (A008578 i))) ((= (modulo n 2) p) (loop (floor->exact (/ n 2)) i (modulo n 2) (* z (A008578 i)))) (else (loop (floor->exact (/ n 2)) (1+ i) (modulo n 2) z)))))

(define (A008578 n) (cond ((< n 3) (1+ n)) (else (list-ref (primes> 0 n) (-1+ n)))))

Inverse of A075158. a(n) = A075159(n+1)-1. a(A000975(n)) = A006093(n) = A000040(n)-1. Cf. A008578, A056539, A059900, A075162.

Sequence in context: A127522 A048673 A096070 this_sequence A046708 A120255 A059450

Adjacent sequences: A075154 A075155 A075156 this_sequence A075158 A075159 A075160

nonn

Antti Karttunen Sep 13 2002