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 A119608 Let b(1)=0, b(2)= 1. b(2^m +k) = (b(2^m+1-k) + b(k))/2, 1 <= k <= 2^m, m >= 0. a(n) is numerator of b(n). 2
 0, 1, 1, 1, 1, 3, 3, 1, 1, 7, 5, 3, 3, 5, 7, 1, 1, 15, 9, 7, 5, 11, 13, 3, 3, 13, 11, 5, 7, 9, 15, 1, 1, 31, 17, 15, 9, 23, 25, 7, 5, 27, 21, 11, 13, 19, 29, 3, 3, 29, 19, 13, 11, 21, 27, 5, 7, 25, 23, 9, 15, 17, 31, 1, 1, 63, 33, 31, 17, 47, 49, 15, 9, 55, 41, 23, 25, 39, 57, 7, 5, 59, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Denominator of b(n), for n >= 2, is A053644(n-1). LINKS FORMULA From Yosu Yurramendi, Mar 13 2019: (Start) Without a(1) = 0, and shifting the terms one place left: a(2^m) = 1, m >= 0; a(2^(m+1)-1-k) = a(2^m+k), m >= 0, 0 < k < 2^m; a(2^(m+1)+k) = a(2^m+k)+2^(m-floor(log2(k)))*a(k), m >= 0, 0 < k < 2^m. (End) MAPLE A119608 := proc (mmax) local a, b, m, k, bn, i; b := [0, 1] ; for m from 1 to mmax do for k from 1 to 2^m do bn := (b[2^m+1-k]+b[k])/2 ; b := [op(b), bn] ; od ; od ; a := [] ; for i from 1 to nops(b) do a := [op(a), numer(b[i])] ; od ; RETURN(a) ; end: an := A119608(7) : for i from 1 to nops(an) do printf("%d, ", an[i]) ; od ; # R. J. Mathar, Aug 06 2006 PROG (R) maxlevel <- 8 # by choice b <- c(0, 1) for(m in 1:maxlevel) for(k in 1:2^m) b[2^m +k] = (b[2^m+1-k] + b[k])/2 d <- vector() for(m in 0:maxlevel) for(k in 0:(2^m-1)) d[2^m + k] <- 2^m; d <- c(0, d) a <- b*d a[1:100] # Yosu Yurramendi, Feb 05 2019 (R) a <- 1 maxlevel <- 15 # by choice for(m in 1:5) {   a[2^(m+1)-1] <- 1   a[2^(m+1)  ] <- 1   for(k in 1:(2^m-1)){   a[2^(m+1)-1-k] <- a[2^m+k]   a[2^(m+1)  +k] <- a[2^m+k]+2^(m-floor(log2(k)))*a[k] }} a <- c(0, a) a[1:128] # Yosu Yurramendi, Mar 13 2019 CROSSREFS Cf. A053644. Sequence in context: A026515 A075772 A142157 * A196646 A196601 A196578 Adjacent sequences:  A119605 A119606 A119607 * A119609 A119610 A119611 KEYWORD easy,nonn,frac AUTHOR Leroy Quet, Jun 04 2006 EXTENSIONS More terms from R. J. Mathar, Aug 06 2006 STATUS approved

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Last modified November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)