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; with one subtracted from each run length, except for the most significant run of 1's.
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
Offset: 0
Keywords
Links
- Paul Tek (terms 0..10000) & Antti Karttunen, Table of n, a(n) for n = 0..16384
- Index entries for sequences that are permutations of the natural numbers
Crossrefs
Programs
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Haskell
import Data.List (group) a075157 0 = 0 a075157 n = product (zipWith (^) a000040_list rs') - 1 where rs' = reverse $ r : map (subtract 1) rs (r:rs) = reverse $ map length $ group $ a030308_row n -- Reinhard Zumkeller, Aug 04 2014
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PARI
A005811(n) = hammingweight(bitxor(n, n>>1)); \\ This function from Gheorghe Coserea, Sep 03 2015 A286468(n) = { my(p=((n+1)%2), i=0, m=1); while(n>0, if(((n%2)==p), m *= prime(i), p = (n%2); i = i+1); n = n\2); m }; A075157(n) = if(!n,n,(prime(A005811(n))*A286468(n))-1);
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Scheme
(define (A075157 n) (if (zero? n) n (+ -1 (* (A000040 (A005811 n)) (fold-left (lambda (a r) (* (A003961 a) (A000079 (- r 1)))) 1 (binexp->runcount1list n)))))) (define (binexp->runcount1list n) (if (zero? n) (list) (let loop ((n n) (rc (list)) (count 0) (prev-bit (modulo n 2))) (if (zero? n) (cons count rc) (if (eq? (modulo n 2) prev-bit) (loop (floor->exact (/ n 2)) rc (1+ count) (modulo n 2)) (loop (floor->exact (/ n 2)) (cons count rc) 1 (modulo n 2))))))) ;; Or, using the code of A286468: (define (A075157 n) (if (zero? n) n (- (* (A000040 (A005811 n)) (A286468 n)) 1)))
Formula
Extensions
Entry revised, PARI-program added and the old incorrect Scheme-program replaced with a new one by Antti Karttunen, May 17 2017
Comments