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 A246660 Run Length Transform of factorials. 15
 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 24, 1, 1, 1, 2, 1, 1, 2, 6, 2, 2, 2, 4, 6, 6, 24, 120, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 24, 2, 2, 2, 4, 2, 2, 4, 12, 6, 6, 6, 12, 24, 24, 120, 720, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 24, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For the definition of the Run Length Transform see A246595. Only Jordan-Polya numbers (A001013) are terms of this sequence. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 FORMULA a(2^n-1) = n!. a(0) = 1, a(2n) = a(n), a(2n+1) = a(n) * A007814(2n+2). - Antti Karttunen, Sep 08 2014 a(n) = A112624(A005940(1+n)). - Antti Karttunen, May 29 2017 a(n) = A323505(n) / A323506(n). - Antti Karttunen, Jan 17 2019 MATHEMATICA Table[Times @@ (Length[#]!&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 83}] (* Jean-François Alcover, Jul 11 2017 *) PROG (Sage) def RLT(f, n):     return [mul([f(len(d)) for d in Integer(a).binary().split('0') if d != '']) for a in range(n)] A246660_list = lambda len: RLT(lambda n: factorial(n), len) A246660_list(88) (PARI) A246660(n) = { my(i=0, p=1); while(n>0, if(n%2, i++; p = p * i, i = 0); n = n\2); p; }; for(n=0, 8192, write("b246660.txt", n, " ", A246660(n))); \\ Antti Karttunen, Sep 08 2014 (Scheme) ;; A stand-alone loop version, like the Pari-program above: (define (A246660 n) (let loop ((n n) (i 0) (p 1)) (cond ((zero? n) p) ((odd? n) (loop (/ (- n 1) 2) (+ i 1) (* p (+ 1 i)))) (else (loop (/ n 2) 0 p))))) ;; One based on given recurrence, utilizing memoizing definec-macro from my IntSeq-library: (definec (A246660 n) (cond ((zero? n) 1) ((even? n) (A246660 (/ n 2))) (else (* (A007814 (+ n 1)) (A246660 (/ (- n 1) 2)))))) ;; Yet another implementation, using fold: (define (A246660 n) (fold-left (lambda (a r) (* a (A000142 r))) 1 (bisect (reverse (binexp->runcount1list n)) (- 1 (modulo n 2))))) (definec (A000142 n) (if (zero? n) 1 (* n (A000142 (- n 1))))) ;; Other functions are as in A227349 - Antti Karttunen, Sep 08 2014 (Python) from operator import mul from functools import reduce from re import split from math import factorial def A246660(n): ....return reduce(mul, (factorial(len(d)) for d in split('0+', bin(n)[2:]) if d != '')) if n > 0 else 1 # Chai Wah Wu, Sep 09 2014 CROSSREFS Cf. A000142, A001013, A007814, A112624, A323505, A323506. Cf. A003714 (gives the positions of ones). Run Length Transforms of other sequences: A001316, A071053, A227349, A246588, A246595, A246596, A246661, A246674. Sequence in context: A025242 A163982 A246661 * A245405 A233543 A156588 Adjacent sequences:  A246657 A246658 A246659 * A246661 A246662 A246663 KEYWORD nonn,base AUTHOR Peter Luschny, Sep 07 2014 STATUS approved

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Last modified January 19 18:25 EST 2020. Contains 331051 sequences. (Running on oeis4.)