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 A286575 Run-length transform of A001316. 5
 1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 8, 4, 8, 2, 4, 4, 4, 4, 8, 2, 4, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 4, 8, 8, 4, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 2, 4, 4, 4, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 4, 8, 8, 4, 4, 8, 8, 8, 8, 16, 8, 16, 4, 8, 8, 8, 8, 16, 4, 8, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Antti Karttunen, Table of n, a(n) for n = 0..16384 FORMULA a(n) = A037445(A005940(1+n)). a(n) = A000079(A286574(n)). EXAMPLE For n = 0, there are no 1-runs, and thus a(0) = 1 as an empty product. For n = 29, "11101" in binary, there are two 1-runs, of lengths 1 and 3, thus a(29) = A001316(1) * A001316(3) = 2*4 = 8. MATHEMATICA Table[Times @@ Map[Sum[Mod[#, 2] &@ Binomial[#, k], {k, 0, #}] &@ Length@ # &, DeleteCases[Split@ IntegerDigits[n, 2], _?(First@ # == 0 &)]], {n, 0, 108}] (* Michael De Vlieger, May 29 2017 *) PROG (Scheme) (define (A286575 n) (fold-left (lambda (a r) (* a (A001316 r))) 1 (bisect (reverse (binexp->runcount1list n)) (- 1 (modulo n 2))))) (define (bisect lista parity) (let loop ((lista lista) (i 0) (z (list))) (cond ((null? lista) (reverse! z)) ((eq? i parity) (loop (cdr lista) (modulo (1+ i) 2) (cons (car lista) z))) (else (loop (cdr lista) (modulo (1+ i) 2) z))))) (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))))))) (define (A001316 n) (let loop ((n n) (z 1)) (cond ((zero? n) z) ((even? n) (loop (/ n 2) z)) (else (loop (/ (- n 1) 2) (* z 2)))))) (Python) from sympy import factorint, prime, log import math def wt(n): return bin(n).count("1") def a037445(n):     f=factorint(n)     return 2**sum([wt(f[i]) for i in f]) def A(n): return n - 2**int(math.floor(log(n, 2))) def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n)) def a(n): return a037445(b(n)) # Indranil Ghosh, May 30 2017 CROSSREFS Cf. A000079, A001316, A005940, A037445, A227349, A247282, A286574. Sequence in context: A286324 A318472 A186643 * A270438 A318836 A003036 Adjacent sequences:  A286572 A286573 A286574 * A286576 A286577 A286578 KEYWORD nonn,base AUTHOR Antti Karttunen, May 28 2017 STATUS approved

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Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)