A153154 - OEIS

%I #16 Oct 08 2021 23:57:31

%S 0,1,3,2,7,4,5,6,15,8,9,14,11,12,13,10,31,16,17,30,19,28,29,18,23,24,

%T 25,22,27,20,21,26,63,32,33,62,35,60,61,34,39,56,57,38,59,36,37,58,47,

%U 48,49,46,51,44,45,50,55,40,41,54,43,52,53,42,127,64,65,126,67,124

%N Permutation of natural numbers: A059893-conjugate of A006068.

%C A002487(1+a(n)) = A020651(n) and A002487(a(n)) = A020650(n). So, it generates the enumeration system of positive rationals based on Stern's sequence A002487. - _Yosu Yurramendi_, Feb 26 2020

%H A. Karttunen, <a href="/A153154/b153154.txt">Table of n, a(n) for n = 0..2047</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F From _Yosu Yurramendi_, Feb 26 2020: (Start)

%F a(1) = 1, for all n > 0 a(2*n) = 2*a(n) + 1, a(2*n+1) = 2*a(A065190(n)).

%F a(1) = 1, a(2) = 3, a(3) = 2, for all n > 1 a(2*n) = 2*a(n) + 1, and if n even a(2*n+1) = 2*a(n+1), else a(2*n+1) = 2*a(n-1).

%F a(n) = A054429(A231551(n)) = A231551(A065190(n)) = A284459(A054429(n)) =

%F        A332769(A284459(n)) = A258996(A154437(n)). (End)

%o (R)

%o maxn <- 63 # by choice

%o a <- c(1,3,2)

%o #

%o for(n in 2:maxn){

%o   a[2*n] <- 2*a[n] + 1

%o   if(n%%2==0) a[2*n+1] <- 2*a[n+1]

%o   else        a[2*n+1] <- 2*a[n-1]

%o }

%o (a <- c(0,a))

%o # _Yosu Yurramendi_, Feb 26 2020

%o (R)

%o # Given n, compute a(n) by taking into account the binary representation of n

%o maxblock <- 8 # by choice

%o a <- c(1, 3, 2)

%o for(n in 4:2^maxblock){

%o   ones <- which(as.integer(intToBits(n)) == 1)

%o   nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)]

%o   anbit <- nbit

%o   for(i in 2:(length(anbit) - 1))

%o     anbit[i] <- bitwXor(anbit[i], anbit[i - 1])  # ?bitwXor

%o   anbit[0:(length(anbit) - 1)] <- 1 - anbit[0:(length(anbit) - 1)]

%o   a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))

%o }

%o (a <- c(0, a))

%o # _Yosu Yurramendi_, Oct 04 2021

%Y Inverse: A153153. a(n) = A059893(A006068(A059893(n))).

%K nonn,base

%O 0,3

%A _Antti Karttunen_, Dec 20 2008