A075157 - OEIS

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A075157

Run lengths in the binary expansion of n gives the vector of exponents in prime factorization of a(n)+1, with the least significant run corresponding to the exponent of the least prime, 2.

0, 1, 2, 3, 5, 4, 8, 7, 11, 14, 6, 9, 17, 24, 26, 15, 23, 44, 34, 29, 13, 10, 20, 19, 35, 74, 48, 49, 53, 124, 80, 31, 47, 134, 174, 89, 69, 76, 104, 59, 27, 32, 12, 21, 41, 54, 62, 39, 71, 224, 244, 149, 97, 120, 146, 99, 107, 374, 342, 249, 161, 624, 242, 63, 95, 404 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`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).`
	LINKS	`Index entries for sequences that are permutations of the natural numbers`
	PROG	`(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)))))`
	CROSSREFS	`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 * A183080 A183082 A183209` `Adjacent sequences: A075154 A075155 A075156 * A075158 A075159 A075160`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen Sep 13 2002`

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Last modified February 14 11:36 EST 2012. Contains 205623 sequences.