A006068 -id:A006068 - cp's OEIS frontend

A324386 a(n) = A324383(A006068(n)).

1, 1, 2, 1, 2, 2, 2, 1, 4, 4, 4, 2, 2, 6, 6, 1, 2, 4, 8, 4, 4, 6, 12, 2, 8, 6, 10, 6, 22, 10, 8, 1, 4, 4, 6, 2, 8, 6, 8, 4, 6, 12, 14, 2, 16, 10, 16, 2, 8, 16, 4, 6, 14, 8, 24, 6, 30, 18, 20, 6, 26, 18, 26, 1, 6, 8, 8, 4, 12, 12, 6, 8, 12, 14, 18, 4, 20, 20, 20, 4, 16, 16, 8, 12, 28, 16, 10, 12, 22, 26, 14, 12, 34, 20, 22, 2, 12

Offset: 0

Antti Karttunen, Feb 27 2019

nonn

This is most likely equal to A276150(A086141(n)), apart from the different offset used in A086141.

The same comments about the parity of terms as in A324383 and A324387 apply also here, except here 1's occur at positions given by 2^k - 1.

Cf. A002110, A006068, A025487, A086141, A276150, A322827, A324342, A324382.

Cf. also A324383, A324387 (permutations of this sequence) and A324380, A324390.

A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A322827(n) = if(!n,1,my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2,#bits,if(bits[i]==bits[i-1], rl++, listput(o,rl))); listput(o,rl); my(es=Vecrev(Vec(o)), m=1); for(i=1,#es,m *= prime(i)^es[i]); (m));
A324383(n) = A276150(A322827(n));
A324386(n) = A324383(A006068(n));

a(n) = A324383(A006068(n)) = A276150(A322827(A006068(n))).

a(A000225(n)) = 1 for all n.

A268725 Square array A(i,j) = A003188(A006068(i) * A006068(j)), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

1, 2, 2, 3, 13, 3, 4, 5, 5, 4, 5, 31, 6, 31, 5, 6, 27, 9, 9, 27, 6, 7, 10, 10, 41, 10, 10, 7, 8, 8, 12, 63, 63, 12, 8, 8, 9, 59, 15, 18, 54, 18, 15, 59, 9, 10, 63, 17, 50, 20, 20, 50, 17, 63, 10, 11, 54, 18, 93, 17, 24, 17, 93, 18, 54, 11, 12, 52, 20, 83, 119, 30, 30, 119, 83, 20, 52, 12, 13, 20, 23, 126, 126, 34, 21, 34, 126, 126, 23, 20, 13

Offset: 1

Antti Karttunen, Feb 13 2016

			The top left [1 .. 15] x [1 .. 15] section of the array:
   1,  2,  3,   4,   5,  6,   7,   8,   9,  10,  11,  12,  13,  14,  15
   2, 13,  5,  31,  27, 10,   8,  59,  63,  54,  52,  20,  22,  49,  17
   3,  5,  6,   9,  10, 12,  15,  17,  18,  20,  23,  24,  27,  29,  30
   4, 31,  9,  41,  63, 18,  50,  93,  83, 126, 118,  36,  32, 107, 101
   5, 27, 10,  63,  54, 20,  17, 119, 126, 108, 105,  40,  45,  99,  34
   6, 10, 12,  18,  20, 24,  30,  34,  36,  40,  46,  48,  54,  58,  60
   7,  8, 15,  50,  17, 30,  21, 110, 101,  34,  97,  60,  59,  44,  43
   8, 59, 17,  93, 119, 34, 110, 145, 187, 238, 162,  68, 196, 247, 221
   9, 63, 18,  83, 126, 36, 101, 187, 166, 252, 237,  72,  65, 215, 202
  10, 54, 20, 126, 108, 40,  34, 238, 252, 216, 210,  80,  90, 198,  68
  11, 52, 23, 118, 105, 46,  97, 162, 237, 210, 253,  92,  79, 200, 195
  12, 20, 24,  36,  40, 48,  60,  68,  72,  80,  92,  96, 108, 116, 120
  13, 22, 27,  32,  45, 54,  59, 196,  65,  90,  79, 108, 121,  82, 119
  14, 49, 29, 107,  99, 58,  44, 247, 215, 198, 200, 116,  82,  69,  89
  15, 17, 30, 101,  34, 60,  43, 221, 202,  68, 195, 120, 119,  89,  86

Antti Karttunen, Table of n, a(n) for n = 1..15051; the first 173 antidiagonals of the array

Cf. A003188, A006068, A268724.
Cf. A268723 (main diagonal).
Cf. A268722 (row 2 and column 2).
Cf. A001969 (row 3 and column 3).
Cf. also A268715.

(define (A268725 n) (A268725bi (A002260 n) (A004736 n)))
(define (A268725bi row col) (A003188 (* (A006068 row) (A006068 col))))

A(i,j) = A003188(A006068(i) * A006068(j)).

A(i,j) = A003188(A268724(i,j)).

A369042 LCM-transform of the inverse of binary Gray code (A006068).

Original entry on oeis.org

1, 3, 2, 7, 1, 2, 5, 1, 1, 1, 13, 2, 3, 11, 1, 31, 1, 1, 29, 1, 5, 3, 1, 2, 17, 19, 1, 23, 1, 1, 1, 1, 1, 1, 61, 1, 1, 59, 1, 1, 7, 1, 1, 1, 1, 1, 53, 2, 1, 1, 1, 1, 1, 1, 37, 47, 1, 1, 1, 1, 41, 43, 1, 127, 1, 1, 5, 1, 11, 1, 1, 1, 113, 1, 1, 1, 1, 1, 1, 1, 97, 1, 1, 103, 1, 1, 101, 1, 1, 1, 109, 1, 1, 107, 1, 2, 1

Offset: 1

Antti Karttunen, Jan 12 2024

nonn

Inverse of Binary Gray code, A006068, is a permutation related to the binary expansion of n that keeps all the numbers of range [2^k, 2^(1+k)[ in the same range, i.e., for all n >= 1, A000523(A006068(n)) = A000523(n), from which it immediately follows that A006068 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A006068(n)), for n >= 1.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A006068, A014963, A368900, A369041, A369043, A369044.

up_to = 65537; \\ Checked up to 2^17;
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2,len, g[n] = lcm(g[n-1],v[n]); b[n] = g[n]/g[n-1]); (b); };
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
v369042 = LCMtransform(vector(up_to,i,A006068(i)));
A369042(n) = v369042[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

a(n) = lcm {1..A006068(n)} / lcm {1..A006068(n-1)}.

a(n) = A014963(A006068(n)). [See comments.]

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

Antti Karttunen, Dec 20 2008

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

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

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

# 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

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)

A268714 Square array A(i,j) = A006068(i) + A006068(j), read by antidiagonals.

Original entry on oeis.org

0, 1, 1, 3, 2, 3, 2, 4, 4, 2, 7, 3, 6, 3, 7, 6, 8, 5, 5, 8, 6, 4, 7, 10, 4, 10, 7, 4, 5, 5, 9, 9, 9, 9, 5, 5, 15, 6, 7, 8, 14, 8, 7, 6, 15, 14, 16, 8, 6, 13, 13, 6, 8, 16, 14, 12, 15, 18, 7, 11, 12, 11, 7, 18, 15, 12, 13, 13, 17, 17, 12, 10, 10, 12, 17, 17, 13, 13, 8, 14, 15, 16, 22, 11, 8, 11, 22, 16, 15, 14, 8, 9, 9, 16, 14, 21, 21, 9, 9, 21, 21, 14, 16, 9, 9

Offset: 0

Antti Karttunen, Feb 12 2016

			The top left [0 .. 15] x [0 .. 15] section of the array:
   0,  1,  3,  2,  7,  6,  4,  5, 15, 14, 12, 13,  8,  9, 11, 10
   1,  2,  4,  3,  8,  7,  5,  6, 16, 15, 13, 14,  9, 10, 12, 11
   3,  4,  6,  5, 10,  9,  7,  8, 18, 17, 15, 16, 11, 12, 14, 13
   2,  3,  5,  4,  9,  8,  6,  7, 17, 16, 14, 15, 10, 11, 13, 12
   7,  8, 10,  9, 14, 13, 11, 12, 22, 21, 19, 20, 15, 16, 18, 17
   6,  7,  9,  8, 13, 12, 10, 11, 21, 20, 18, 19, 14, 15, 17, 16
   4,  5,  7,  6, 11, 10,  8,  9, 19, 18, 16, 17, 12, 13, 15, 14
   5,  6,  8,  7, 12, 11,  9, 10, 20, 19, 17, 18, 13, 14, 16, 15
  15, 16, 18, 17, 22, 21, 19, 20, 30, 29, 27, 28, 23, 24, 26, 25
  14, 15, 17, 16, 21, 20, 18, 19, 29, 28, 26, 27, 22, 23, 25, 24
  12, 13, 15, 14, 19, 18, 16, 17, 27, 26, 24, 25, 20, 21, 23, 22
  13, 14, 16, 15, 20, 19, 17, 18, 28, 27, 25, 26, 21, 22, 24, 23
   8,  9, 11, 10, 15, 14, 12, 13, 23, 22, 20, 21, 16, 17, 19, 18
   9, 10, 12, 11, 16, 15, 13, 14, 24, 23, 21, 22, 17, 18, 20, 19
  11, 12, 14, 13, 18, 17, 15, 16, 26, 25, 23, 24, 19, 20, 22, 21
  10, 11, 13, 12, 17, 16, 14, 15, 25, 24, 22, 23, 18, 19, 21, 20

Antti Karttunen, Table of n, a(n) for n = 0..15050; the first 173 antidiagonals of the array

Cf. A003188, A268715.
Cf. A006068 (row 0, column 0).
Cf. A066194 (row 1, column 1).
Cf. A268716 (main diagonal).
Cf. also A268724.

A006068[n_] := BitXor @@ Table[Floor[n/2^m], {m, 0, Log[2, n]}]; A006068[0] = 0; A[i_, j_] := A006068[i] + A006068[j]; Table[A[i-j, j], {i, 0, 13}, {j, 0, i}] // Flatten (* Jean-François Alcover, Feb 17 2016 *)

\\ Produces the triangle when the array is read by antidiagonals
a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2); /* A006068 */
T(i,j) = a(i) + a(j);
for(i=0, 13, for(j=0, i, print1(T(i - j, j),", "););print();); \\ Indranil Ghosh, Mar 23 2017

# Produces the triangle when the array is read by antidiagonals
def A006068(n):
    return n if n<2 else 2*A006068(n//2) + (n%2 + A006068(n//2)%2)%2
def T(i,j): return A006068(i) + A006068(j)
for i in range(14):
    print([T(i - j, j) for j in range(i + 1)]) # Indranil Ghosh, Mar 23 2017

(define (A268714 n) (A268714bi (A002262 n) (A025581 n)))
(define (A268714bi row col) (+ (A006068 row) (A006068 col)))

A(i,j) = A006068(i) + A006068(j).

A(i,j) = A006068(A268715(i,j)). - Corrected Mar 23 2017

A268724 Square array A(i,j) = A006068(i) * A006068(j), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

1, 3, 3, 2, 9, 2, 7, 6, 6, 7, 6, 21, 4, 21, 6, 4, 18, 14, 14, 18, 4, 5, 12, 12, 49, 12, 12, 5, 15, 15, 8, 42, 42, 8, 15, 15, 14, 45, 10, 28, 36, 28, 10, 45, 14, 12, 42, 30, 35, 24, 24, 35, 30, 42, 12, 13, 36, 28, 105, 30, 16, 30, 105, 28, 36, 13, 8, 39, 24, 98, 90, 20, 20, 90, 98, 24, 39, 8, 9, 24, 26, 84, 84, 60, 25, 60, 84, 84, 26, 24, 9

Offset: 1

Antti Karttunen, Feb 13 2016

			The top left [1 .. 15] x [1 .. 15] section of the array:
   1,  3,  2,  7,   6,  4,  5,  15,  14,  12,  13,   8,   9,  11,  10
   3,  9,  6,  21, 18, 12, 15,  45,  42,  36,  39,  24,  27,  33,  30
   2,  6,  4,  14, 12,  8, 10,  30,  28,  24,  26,  16,  18,  22,  20
   7, 21, 14,  49, 42, 28, 35, 105,  98,  84,  91,  56,  63,  77,  70
   6, 18, 12,  42, 36, 24, 30,  90,  84,  72,  78,  48,  54,  66,  60
   4, 12,  8,  28, 24, 16, 20,  60,  56,  48,  52,  32,  36,  44,  40
   5, 15, 10,  35, 30, 20, 25,  75,  70,  60,  65,  40,  45,  55,  50
  15, 45, 30, 105, 90, 60, 75, 225, 210, 180, 195, 120, 135, 165, 150
  14, 42, 28,  98, 84, 56, 70, 210, 196, 168, 182, 112, 126, 154, 140
  12, 36, 24,  84, 72, 48, 60, 180, 168, 144, 156,  96, 108, 132, 120
  13, 39, 26,  91, 78, 52, 65, 195, 182, 156, 169, 104, 117, 143, 130
   8, 24, 16,  56, 48, 32, 40, 120, 112,  96, 104,  64,  72,  88,  80
   9, 27, 18,  63, 54, 36, 45, 135, 126, 108, 117,  72,  81,  99,  90
  11, 33, 22,  77, 66, 44, 55, 165, 154, 132, 143,  88,  99, 121, 110
  10, 30, 20,  70, 60, 40, 50, 150, 140, 120, 130,  80,  90, 110, 100

Antti Karttunen, Table of n, a(n) for n = 1..15051; the first 173 antidiagonals of the array

Cf. A268725.
Cf. A006068 (row 1, column 1).
Cf. A268716 (row 3, column 3).
Cf. A268721 (the antidiagonal sums).
Cf. also A268714.

(define (A268724 n) (A268724bi (A002260 n) (A004736 n)))
(define (A268724bi row col) (* (A006068 row) (A006068 col)))

A(i,j) = A006068(i) * A006068(j)

A(i,j) = A006068(A268725(i,j)).

A277808 a(n) = number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 6, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4

Offset: 1

Antti Karttunen, Nov 03 2016

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

One less than A277822.
A left inverse of A003945.
Cf. A277812 (gives the odious number where such an iteration is finished at when starting from k=n).
Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A268389.

a(n) = A010059(n) * A001511(n).
If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = 0, otherwise a(n) = 1 + a(A003188(A006068(n)/2)).
Other identities:
For all n >= 0, a(A003945(n)) = n.

A302029 Inverse permutation of A207901: a(n) = A006068(A052331(n)).

Original entry on oeis.org

0, 1, 3, 7, 15, 2, 31, 6, 63, 14, 127, 4, 255, 30, 12, 511, 1023, 62, 2047, 8, 28, 126, 4095, 5, 8191, 254, 60, 24, 16383, 13, 32767, 510, 124, 1022, 16, 56, 65535, 2046, 252, 9, 131071, 29, 262143, 120, 48, 4094, 524287, 508, 1048575, 8190, 1020, 248, 2097151, 61, 112, 25, 2044, 16382, 4194303, 11, 8388607, 32766, 32

Offset: 1

Antti Karttunen, Apr 13 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4096
Index entries for sequences that are permutations of the natural numbers

Inverse of A207901.

One less than A302030.

up_to = 4096;
v050376 = vector(up_to);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to,break));
A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A302029(n) = A006068(A052331(n));

a(n) = A006068(A052331(n)).

A302843 Permutation of nonnegative integers: a(n) = A163355(A006068(n)).

Original entry on oeis.org

0, 1, 2, 3, 12, 13, 14, 15, 10, 9, 8, 11, 4, 7, 6, 5, 26, 27, 24, 25, 30, 29, 28, 31, 16, 19, 18, 17, 22, 23, 20, 21, 42, 43, 40, 41, 46, 45, 44, 47, 32, 35, 34, 33, 38, 39, 36, 37, 58, 57, 56, 59, 52, 55, 54, 53, 48, 49, 50, 51, 60, 61, 62, 63, 192, 193, 194, 195, 204, 205, 206, 207, 202, 201, 200, 203, 196, 199, 198, 197, 218, 219, 216, 217, 222

Offset: 0

Antti Karttunen, Apr 14 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences that are permutations of the natural numbers

Cf. A302844 (inverse).

Cf. A003188, A006068, A057300, A163355, A302845.

A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A057300(n) = { my(t=1, s=0); while(n>0,  if(1==(n%4),n++,if(2==(n%4),n--)); s += (n%4)*t; n >>= 2; t <<= 2); (s); };
A163355(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); if(((1==d)&&!(i%2))||((2==d)&&(i%2)), f+A163355(A057300(r)), if(3==d,f+f+A163355(A057300(r)), (3*f)+A163355(f-1-r))));
A302843(n) = A163355(A006068(n));

a(n) = A163355(A006068(n)).

a(n) = A302845(A003188(n)).

A245452 Self-inverse permutation of nonnegative integers, A075158-conjugate of the inverse of gray code: a(n) = 1 + A075157(A006068(A075158(n-1))).

Original entry on oeis.org

1, 2, 4, 3, 9, 8, 18, 5, 6, 25, 75, 16, 150, 36, 27, 7, 735, 12, 1470, 49, 50, 245, 12705, 32, 15, 300, 10, 72, 25410, 125, 195195, 11, 225, 4235, 54, 24, 390390, 2940, 490, 121, 4339335, 100, 8678670, 847, 81, 65065, 92147055, 64, 30, 35, 2205, 600, 184294110, 20, 147, 144, 8470, 50820, 2565568005, 343, 5131136010, 1446445, 98, 13

Offset: 1

Antti Karttunen, Jul 22 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers

Inverse: A245451.
Cf. A006068, A075157, A075158.
Similar permutations: A245454, A122111, A241909, A241916.

(define (A245452 n) (+ 1 (A075157 (A006068 (A075158 (- n 1))))))

a(n) = 1 + A075157(A006068(A075158(n-1))).

cp's OEIS Frontend

A324386 a(n) = A324383(A006068(n)).

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A268725 Square array A(i,j) = A003188(A006068(i) * A006068(j)), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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Formula

A369042 LCM-transform of the inverse of binary Gray code (A006068).

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PARI

Formula

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

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R

R

Formula

A268714 Square array A(i,j) = A006068(i) + A006068(j), read by antidiagonals.

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Mathematica

PARI

Python

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Formula

A268724 Square array A(i,j) = A006068(i) * A006068(j), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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Formula

A277808 a(n) = number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

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A302029 Inverse permutation of A207901: a(n) = A006068(A052331(n)).

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PARI