A258996 -id:A258996 - cp's OEIS frontend

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A092569 Permutation of integers a(a(n)) = n. In binary representation of n, transformation of inner bits, 1 <-> 0, gives binary representation of a(n).

0, 1, 2, 3, 6, 7, 4, 5, 14, 15, 12, 13, 10, 11, 8, 9, 30, 31, 28, 29, 26, 27, 24, 25, 22, 23, 20, 21, 18, 19, 16, 17, 62, 63, 60, 61, 58, 59, 56, 57, 54, 55, 52, 53, 50, 51, 48, 49, 46, 47, 44, 45, 42, 43, 40, 41, 38, 39, 36, 37, 34, 35, 32, 33, 126, 127, 124, 125, 122, 123, 120

Offset: 0

Zak Seidov, Feb 28 2004

Primes which stay primes under transformation "opposite inner bits", A092570.
This permutation transforms the enumeration system of positive irreducible fractions A020651/A020650 into the enumeration system A245327/A245326, and vice versa. - Yosu Yurramendi, Jun 16 2015
A117120(a(n)) = a(A117120(n)), n > 0.
A258996(a(n)) = a(A258996(n)), n > 0.
A258746(a(n)) = a(A258746(n)), n > 0.
A054429(a(n)) = a(A054429(n)), n > 0.
a(n) = A054429(A065190(n)) = A065190(A054429(n)), n > 0. - Yosu Yurramendi, Mar 23 2017

			a(9)=15 because 9_10 = 1001_2, transformation of inner bits gives 1001_2 -> 1111_2 = 15_10.

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A092570.

bb={0, 1, 2, 3};Do[id=IntegerDigits[n, 2];Do[id[[i]]=1-id[[i]], {i, 2, Length[id]-1}];bb=Append[bb, FromDigits[id, 2]], {n, 4, 1000}];fla=Flatten[bb]
(* Second program: *)
Table[If[n < 2, n, Function[b, FromDigits[#, 2] &@ Join[{First@ b}, Most[Rest@ b] /. { 0 -> 1, 1 -> 0}, {Last@ b}]]@ IntegerDigits[n, 2]], {n, 0, 70}] (* Michael De Vlieger, Apr 03 2017 *)

T(n)={pow2=2;v=binary(n);L=#v-1;forstep(k=L,2,-1,if(v[k],n-=pow2,n+=pow2);pow2*=2);return(n)};
for(n=0,70,print1(T(n),", ")) \\ Washington Bomfim, Jan 18 2011

maxrow <- 8 # by choice
a <- 1:3 # If it were c(1, 3, 2), it would be A054429
for(m in 1:maxrow) for(k in 0:(2^m-1)){
a[2^(m+1)+    k] = a[2^m+k] + 2^(m+1)
a[2^(m+1)+2^m+k] = a[2^m+k] + 2^m
}
a
# Yosu Yurramendi, Apr 10 2017

a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3, a(2^(m+1) +k) = a(2^m+k) + 2^(m+1),

a(2^(m+1)+2^m+k) = a(2^m+k) + 2^m, m >= 1, 0 <= k < 2^m. - Yosu Yurramendi, Apr 02 2017

A117120 a(1)=1. a(n) is smallest positive integer not occurring earlier in the sequence where a(n) is congruent to -1 (mod a(n-1)).

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 11, 10, 9, 8, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 95, 94, 93, 92, 91, 90, 89, 88, 87

Offset: 1

Leroy Quet, Apr 19 2006

Sequence is a permutation of the positive integers.
The permutation is self-inverse. Except for fixed points 1, 2, 3 it consists completely of 2-cycles: (4,5), (6,7), (8,11), (9,10), (12,15), (13,14), (16,23), (17,22), ..., (24,31), ..., (32,47), ... . - Klaus Brockhaus
The permutation transforms enumeration system of positive irreducible fractions A071766/A229742 (HCS) into enumeration system A245325/A245326, and vice versa. - Yosu Yurramendi, Jun 09 2015
A092569(a(n)) = a(A092569(n)), n > 0.
A258746(a(n)) = a(A258746(n)), n > 0.
A258996(a(n)) = a(A258996(n)), n > 0.
A054429(a(n)) = a(A054429(n)), n > 0.
a(n) = A054429(A063946(n)) = A063946(A054429(n)), n > 0. - Yosu Yurramendi, Mar 23 2017

Cf. A071766, A229742, A245325, A245326.

A[1]:= 1: A[2]:= 2: B[1]:= 0: B[2]:= 0:
for n from 3 to 100 do
  for m from A[n-1]-1 by A[n-1] while assigned(B[m]) do od:
  A[n]:= m;
  B[m]:= 0;
od:
seq(A[n],n=1..100); # Robert Israel, Jun 09 2015

f[n_] := Block[{a = {1}, i, k}, Do[k = 1; While[Or[Mod[k, a[[i - 1]]] != a[[i - 1]] - 1, MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, n}]; a]; f@ 120 (* Michael De Vlieger, Jun 11 2015 *)
A[n_]:= If[n<4, n, If[EvenQ[n], 2A[n/2] + 1, 2A[(n - 1)/2]]]; Table[A[n], {n, 100}] (* Indranil Ghosh, Mar 21 2017 *)
f[lst_List] := Block[{k = 2, m = lst[[-1]]}, While[ MemberQ[lst, k] || 1 + Mod[k, m] != m, k++]; Append[lst, k]]; Nest[f, {1}, 70] (* Robert G. Wilson v, Jan 22 2018 *)

A(n) = if(n<4, n, if(n%2, 2*A(n\2), 2*A(n/2)+1));
for(n=1, 50, print1(A(n), ", ")) \\ Indranil Ghosh, Mar 21 2017

a <- 1:3 # If it were c(1, 3, 2), it would be A054429
maxn <- 50 # by choice
#
for(n in 2:maxn){
  a[2*n  ] <- 2*a[n]+1
  a[2*n+1] <- 2*a[n]
}
#
a
# Yosu Yurramendi, Jun 08 2015

For n >= 2: If a(n-1) = 2^m, m=positive integer, then a(n)= 2^(m+1)-1. If a(n-1) = 3*2^m, m= nonnegative integer, then a(n) = 3*2^(m+1)-1. Otherwise, a(n) = a(n-1) -1.

For n >= 2: a(2*n) = 2*a(n)+1, a(2*n+1) = 2*a(n). - Yosu Yurramendi, Jun 08 2015

More terms from Klaus Brockhaus

A284459 Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A245327/A245328, and A162911/A162912 (Drib) into A020651/A020650 (Yu-Ting inverted).

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 7, 10, 13, 12, 11, 14, 9, 8, 15, 26, 21, 20, 27, 22, 25, 24, 23, 18, 29, 28, 19, 30, 17, 16, 31, 42, 53, 52, 43, 54, 41, 40, 55, 50, 45, 44, 51, 46, 49, 48, 47, 58, 37, 36, 59, 38, 57, 56, 39, 34, 61, 60, 35, 62, 33, 32, 63

Offset: 1

Yosu Yurramendi, Mar 27 2017

nonn

The inverse permutation is A284460.

Yosu Yurramendi, Table of n, a(n) for n = 1..16383
Index entries for sequences that are permutations of the natural numbers

Cf. A002487, A020650, A020651, A162911, A162912, A245327, A245328, A284460.

maxrow <- 12 # by choice
a <- 1
b01 <- 1
for(m in 0:maxrow){
  b01 <- c(b01, c(1-b01[2^m:(2^(m+1)-1)], b01[2^m:(2^(m+1)-1)]) )
  for(k in 0:(2^m-1)){
    a[2^(m+1) +       k] <- a[2^m + k] + 2^(m + b01[2^(m+1) +       k])
    a[2^(m+1) + 2^m + k] <- a[2^m + k] + 2^(m + b01[2^(m+1) + 2^m + k])
}}
a
# Yosu Yurramendi, Mar 27 2017

maxblock <- 7 # by choice
a <- 1:3
for(n in 4:2^maxblock){
ones <- which(as.integer(intToBits(n)) == 1)
nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)]
anbit <- nbit
for(i in 2:(length(anbit) - 1))
   anbit[i] <- 1 - bitwXor(anbit[i], anbit[i-1])
a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))
}
a
# Yosu Yurramendi, Apr 25 2021

a(n) = A258996(A231551(n)) = A231551(A092569(n)), n > 0 . - Yosu Yurramendi, Apr 10 2017

A231551 Position of n in A231550.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 8, 15, 14, 9, 12, 11, 10, 13, 16, 31, 30, 17, 28, 19, 18, 29, 24, 23, 22, 25, 20, 27, 26, 21, 32, 63, 62, 33, 60, 35, 34, 61, 56, 39, 38, 57, 36, 59, 58, 37, 48, 47, 46, 49, 44, 51, 50, 45, 40, 55, 54, 41, 52, 43, 42, 53, 64, 127, 126, 65

Offset: 0

Alex Ratushnyak, Nov 10 2013

This permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A020651/A020650, and A162911/A162912 (Drib) the enumeration system into A245327/A245326. - Yosu Yurramendi, Jun 16 2015

Cf. A003188, A006068, A231550.

Join[{0, 1}, Table[d = Reverse@IntegerDigits[n, 2]; FromDigits[Reverse@Append[FoldList[BitXor, d[[1]], Most@Rest@d], d[[-1]]], 2], {n, 2, 67}]] (* Ivan Neretin, Dec 28 2016 *)

for n in range(99):
  bits = [0]*64
  orig = [0]*64
  l = int.bit_length(int(n))
  t = n
  for i in range(l):
    bits[i] = orig[i] = t&1
    t>>=1
  #for i in range(1, l-1):  bits[i] ^= orig[i-1]   # A231550
  for i in range(1, l-1):  bits[i] ^= bits[i-1]   # A231551
  #for i in range(l-1):  bits[i] ^= orig[i+1]      # A003188
  #for i in range(1, l):  bits[l-1-i] ^= bits[l-i]  # A006068
  t = 0
  for i in range(l):  t += bits[i]<

R

maxrow <- 8 # by choice b01 <- 0 # b01 is going to be A010059 a <- 1 for(m in 0:maxrow) for(k in 0:(2^m-1)){ b01[2^(m+1)+ k] <- b01[2^m+k] a[2^(m+1)+ k] <- a[2^m+k] + 2^(m+b01[2^(m+1)+ k]) b01[2^(m+1)+2^m+k] <- 1 - b01[2^m+k] a[2^(m+1)+2^m+k] <- a[2^m+k] + 2^(m+b01[2^(m+1)+2^m+k]) } (a <- c(0,a)) # Yosu Yurramendi, Apr 10 2017

R

maxblock <- 8 # by choice a <- 1:3 for(n in 4:2^maxblock){ ones <- which(as.integer(intToBits(n)) == 1) nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)] anbit <- nbit for(i in 2:(length(anbit) - 1)) anbit[i] <- bitwXor(anbit[i], anbit[i-1]) # ?bitwXor a <- c(a, sum(anbit*2^(0:(length(anbit) - 1)))) } (a <- c(0,a)) # Yosu Yurramendi, Apr 25 2021

Formula

A231550(a(n)) = a(A231550(n)) = n.

a(n) = A258996(A284460(n)) = A284459(A092569(n)), n > 0. - Yosu Yurramendi, Apr 10 2017

a(n) = A054429(A153154(n)), n > 0. - Yosu Yurramendi, Oct 04 2021

A268087 a(n) = A162909(n) + A162910(n).

Original entry on oeis.org

2, 3, 3, 5, 4, 4, 5, 8, 7, 5, 7, 7, 5, 7, 8, 13, 11, 9, 12, 9, 6, 10, 11, 11, 10, 6, 9, 12, 9, 11, 13, 21, 18, 14, 19, 16, 11, 17, 19, 14, 13, 7, 11, 17, 13, 15, 18, 18, 15, 13, 17, 11, 7, 13, 14, 19, 17, 11, 16, 19, 14, 18, 21, 34, 29, 23, 31, 25, 17, 27, 30, 25, 23, 13, 20, 29, 22, 26, 31, 23, 19, 17, 22, 13, 8, 16, 17, 27

Offset: 1

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Author

Yosu Yurramendi, Jan 26 2016

Keywords

nonn
easy

Comments

If the terms (n>0) are written as an array (in a left-aligned fashion) with rows of length 2^m, m >= 0:

2,

3, 3,

5, 4, 4, 5,

8, 7, 5, 7, 7, 5, 7, 8,

13,11, 9,12, 9, 6,10,11,11,10,6, 9,12, 9,11,13,

21,18,14,19,16,11,17,19,14,13,7,11,17,13,15,18,18,15,13,17,11,7,13,14,19,17,11,16, ...

a(n) is palindromic in each level m >= 0 (ranks between 2^m and 2^(m+1)-1), because in each level m >= 0 A162910 is the reverse of A162909:

a(2^m + k) = a(2^(m+1) - 1 - k), m >= 0, 0 <= k < 2^m.

All columns have the Fibonacci sequence property: a(2^(m+2) + k) = a(2^(m+1) + k) + a(2^m + k), m >= 0, 0 <= k < 2^m (empirical observations).

a(2^m + k) = A162909(2^(m+2) + k), a(2^m + k) = A162909(2^(m+1)+ 2^m + k), a(2^m + k) = A162910(2^(m+1) + k), m >= 0, 0 <= k < 2^m (empirical observations).

a(n) = A162911(n) + A162912(n), where A162911(n)/A162912(n) is the bit reversal permutation of A162909(n)/A162910(n) in each level m >= 0 (empirical observations).

a(n) = A162911(2n+1), a(n) = A162912(2n) for n > 0 (empirical observations). n > 1 occurs in this sequence phi(n) = A000010(n) times, as it occurs in A007306 (Franklin T. Adams-Watters's comment), which is the sequence obtained by adding numerator and denominator in the Calkin-Wilf enumeration system of positive rationals. A162909(n)/A162910(n) is also an enumeration system of all positive rationals (Bird system), and in each level m >= 0 (ranks between 2^m and 2^(m+1)-1) rationals are the same in both systems. Thus a(n) has the same terms in each level as A007306.

The same property occurs in all numerator+denominator sequences of enumeration systems of positive rationals, as, for example, A007306 (A007305+A047679), A071585 (A229742+A071766), and A086592 (A020650+A020651).

Examples

m = 3, k = 6: a(38) = 17, a(22) = 10, a(14) = 7.

Crossrefs

Cf. A162909, A162910, A162911, A162912, A007306, A071585, A086592.

Programs

PARI

a(n) = my(x=1, y=1); for(i=0, logint(n, 2), if(bittest(n, i), [x, y]=[x+y, x], [x, y]=[y, x+y])); x \\ Mikhail Kurkov, Mar 10 2023

Formula

a(2^(m+2)+k) = a(2^(m+1)+k) + a(2^m+k) with m = 0, 1, 2, ... and 0 <= k < 2^m (empirical observation).

a(A059893(n)) = a(n) for n > 0. - Yosu Yurramendi, May 30 2017

From Yosu Yurramendi, May 14 2019: (Start)

Take the smallest m > 0 such that 0 <= k < 2^(m-1), and choose any M >= m,

a((1/3)*( A016921(2^(m-1)+k)*4^(M-m)-1)) = 2*a(2^(m-1)+k)*(M-m) + a(2^m+2*k ).

a((1/3)*(2*A016921(2^(m-1)+k)*4^(M-m)-2)) = 2*a(2^(m-1)+k)*(M-m) + a(2^m+2*k ) + a(2^(m-1)+k).

a((1/3)*( A016969(2^(m-1)+k)*4^(M-m)-2)) = 2*a(2^(m-1)+k)*(M-m) + a(2^m+2*k+1).

a((1/3)*(2*A016969(2^(m-1)+k)*4^(M-m)-1)) = 2*a(2^(m-1)+k)*(M-m) + a(2^m+2*k+1) + a(2^(m-1)+k). (End)

a(n) = A007306(A258996(n)), n > 0. - Yosu Yurramendi, Jun 23 2021

A153154 Permutation of natural numbers: A059893-conjugate of A006068.

Original entry on oeis.org

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, 25, 22, 27, 20, 21, 26, 63, 32, 33, 62, 35, 60, 61, 34, 39, 56, 57, 38, 59, 36, 37, 58, 47, 48, 49, 46, 51, 44, 45, 50, 55, 40, 41, 54, 43, 52, 53, 42, 127, 64, 65, 126, 67, 124

Offset: 0

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Author

Antti Karttunen, Dec 20 2008

Keywords

nonn
base

Comments

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

Links

A. Karttunen, Table of n, a(n) for n = 0..2047

Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

R

maxn <- 63 # by choice a <- c(1,3,2) # for(n in 2:maxn){ a[2*n] <- 2*a[n] + 1 if(n%%2==0) a[2*n+1] <- 2*a[n+1] else a[2*n+1] <- 2*a[n-1] } (a <- c(0,a)) # Yosu Yurramendi, Feb 26 2020

R

# Given n, compute a(n) by taking into account the binary representation of n maxblock <- 8 # by choice a <- c(1, 3, 2) for(n in 4:2^maxblock){ ones <- which(as.integer(intToBits(n)) == 1) nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)] anbit <- nbit for(i in 2:(length(anbit) - 1)) anbit[i] <- bitwXor(anbit[i], anbit[i - 1]) # ?bitwXor anbit[0:(length(anbit) - 1)] <- 1 - anbit[0:(length(anbit) - 1)] a <- c(a, sum(anbit*2^(0:(length(anbit) - 1)))) } (a <- c(0, a)) # Yosu Yurramendi, Oct 04 2021

Formula

From Yosu Yurramendi, Feb 26 2020: (Start)

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

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).

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

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

A154437 Permutation of nonnegative integers: A059893-conjugate of A154435.

Original entry on oeis.org

0, 1, 3, 2, 5, 6, 7, 4, 13, 10, 11, 12, 9, 14, 15, 8, 21, 26, 27, 20, 25, 22, 23, 24, 29, 18, 19, 28, 17, 30, 31, 16, 53, 42, 43, 52, 41, 54, 55, 40, 45, 50, 51, 44, 49, 46, 47, 48, 37, 58, 59, 36, 57, 38, 39, 56, 61, 34, 35, 60, 33, 62, 63, 32, 85, 106, 107, 84, 105, 86, 87

Offset: 0

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Author

Antti Karttunen, Jan 17 2009

Keywords

nonn
base

Comments

This permutation is induced by the same Lamplighter group generating wreath recursion (binary transducer) as A154435, starting from the active (swapping) state a, but in contrast to it, this one rewrites the bits from the least significant end up to the second most significant bit.

Links

A. Karttunen, Table of n, a(n) for n = 0..2047

Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A154438. a(n) = A059893(A154435(A059893(n))) = A054429(A153154(A054429(n))).

Programs

R

maxn <- 63 # by choice a <- c(1,3,2) for(n in 2:maxn){ a[2*n+1] <- 2*a[n] if(n%%2 == 0) a[2*n] <- 2*a[n+1] + 1 else a[2*n] <- 2*a[n-1] + 1 } (a <- c(0,a)) # Yosu Yurramendi, Feb 23 2020

Formula

From Yosu Yurramendi, Feb 23 2020: (Start)

a(n) = A054429(A284459(n)) = A258996(A153154(n)) = A284459(A065190(n)).

a(1) = 1; for n > 0, a(2*n) = 2*a(A065190(n)) + 1, a(2*n+1) = 2*a(n). (End)

A231550 Permutation of nonnegative integers: for each bit[i] in the binary representation, except the most and the least significant bits, set bit[i] = bit[i] XOR bit[i-1], where bit[i-1] is the less significant bit, XOR is the binary logical exclusive or operator.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 8, 11, 14, 13, 12, 15, 10, 9, 16, 19, 22, 21, 28, 31, 26, 25, 24, 27, 30, 29, 20, 23, 18, 17, 32, 35, 38, 37, 44, 47, 42, 41, 56, 59, 62, 61, 52, 55, 50, 49, 48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33, 64, 67, 70, 69, 76

Offset: 0

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Author

Alex Ratushnyak, Nov 10 2013

Keywords

nonn
look
base
easy

Comments

This permutation transforms the enumeration system of positive irreducible fractions A020651/A020650 into the enumeration system A002487/A002487' (Calkin-Wilf), and enumeration system A245327/A245326 into A162911/A162912 (Drib). - Yosu Yurramendi, Jun 16 2015

Links

Ivan Neretin, Table of n, a(n) for n = 0..8192

Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A003188, A006068, A231551.

Programs

Mathematica

Join[{0, 1}, Table[d = IntegerDigits[n, 2]; FromDigits[Join[{d[[1]]}, BitXor[Most@Rest@d, Rest@Rest@d], {d[[-1]]}], 2], {n, 2, 68}]] (* Ivan Neretin, Dec 28 2016 *)

PARI

a(n) = bitxor(n, if(n>3, bitand(n<<1, bitneg(0,logint(n,2))))); \\ Kevin Ryde, Jul 17 2021

Python

for n in range(99): bits = [0]*64 orig = [0]*64 l = int.bit_length(int(n)) t = n for i in range(l): bits[i] = orig[i] = t&1 t>>=1 for i in range(1, l-1): bits[i] ^= orig[i-1] # A231550 #for i in range(1, l-1): bits[i] ^= bits[i-1] # A231551 #for i in range(l-1): bits[i] ^= orig[i+1] # A003188 #for i in range(1,l): bits[l-1-i] ^= bits[l-i] # A006068 t = 0 for i in range(l): t += bits[i]<

R

a <- 1 maxlevel <- 8 # by choice # for(m in 0:maxlevel) for(k in 0:(2^m-1)){ a[2^(m+1) +2*k] <- 2*a[2^m+k] a[2^(m+2)-1-2*k] <- 2*a[2^m+k] + 1 } (a <- c(0,a)) # Yosu Yurramendi, Apr 10 2017

Formula

a(A231551(n)) = A231551(a(n)) = n.

a(n) = A284460(A258996(n)) = A092569(A284460(n)), n > 0. - Yosu Yurramendi, Apr 10 2017

A284460 Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A245327/A245328 into the enumeration system A002487/A002487' (Calkin-Wilf), and A020651/A020650 (Yu-Ting inverted) into A162911/A162912(Drib).

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 7, 14, 13, 8, 11, 10, 9, 12, 15, 30, 29, 24, 27, 18, 17, 20, 23, 22, 21, 16, 19, 26, 25, 28, 31, 62, 61, 56, 59, 50, 49, 52, 55, 38, 37, 32, 35, 42, 41, 44, 47, 46, 45, 40, 43, 34, 33, 36, 39, 54, 53, 48, 51, 58, 57, 60, 63

Offset: 1

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Yosu Yurramendi, Mar 28 2017

Keywords

nonn

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The inverse permutation is A284459.

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Yosu Yurramendi, Table of n, a(n) for n = 1..16383

Index entries for sequences that are permutations of the natural numbers

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Cf. A002487, A020650, A020651, A162911, A162912, A245327, A245328, A284459.

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maxrow <- 4 # by choice a <- 1 b01 <- 1 for(m in 0:maxrow){ b01 <- c(b01,rep(1,2^(m+1))); b01[(2^(m+1)+2^m-2^(m-1)):(2^(m+1)+2^m+2^(m-1)-1)] <- 0 for(k in 0:(2^m-1)){ a[2^(m+1) + k] <- a[2^m + k] + 2^(m + b01[2^(m+1) + k]) a[2^(m+1) + 2^m + k] <- a[2^m + k] + 2^(m + b01[2^(m+1) + 2^m + k]) }} a # Yosu Yurramendi, Mar 28 2017

Formula

a(n) = A231550(A258996(n)) = A092569(A231550(n)), n > 0 . - Yosu Yurramendi, Apr 10 2017

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A092569 Permutation of integers a(a(n)) = n. In binary representation of n, transformation of inner bits, 1 <-> 0, gives binary representation of a(n).

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A117120 a(1)=1. a(n) is smallest positive integer not occurring earlier in the sequence where a(n) is congruent to -1 (mod a(n-1)).

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A284459 Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A245327/A245328, and A162911/A162912 (Drib) into A020651/A020650 (Yu-Ting inverted).

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A231551 Position of n in A231550.

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A268087 a(n) = A162909(n) + A162910(n).

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A153154 Permutation of natural numbers: A059893-conjugate of A006068.

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A154437 Permutation of nonnegative integers: A059893-conjugate of A154435.

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