A004442 -id:A004442 - cp's OEIS frontend

A004444 Nimsum n + 3.

3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28, 35, 34, 33, 32, 39, 38, 37, 36, 43, 42, 41, 40, 47, 46, 45, 44, 51, 50, 49, 48, 55, 54, 53, 52, 59, 58, 57, 56, 63, 62, 61, 60, 67, 66, 65, 64, 71

Offset: 0

N. J. A. Sloane

The same as A120634 except for first 3 terms. - Pietro Battiston, Jan 19 2008

Permutation of the nonnegative integers. - Wesley Ivan Hurt, Apr 06 2016

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.

Cf. A004442 (nimsum n+1), A004443 (nimsum n+2), A120634.

[n + (-1)^n + 2*(-1)^Floor(n/2): n in [0..100]]; // Wesley Ivan Hurt, Apr 06 2016

A004444:=n->n+(-1)^n+2*(-1)^floor(n/2): seq(A004444(n), n=0..50); # Wesley Ivan Hurt, Apr 06 2016

CoefficientList[Series[(4x^4-x^3-x^2-x+3)/((x-1)^2(x+1) (x^2+1)), {x,0,70}],x] (* Harvey P. Dale, Mar 24 2011 *)
Table[n + (-1)^n + 2 (-1)^Floor[n/2], {n, 0, 100}] (* Wesley Ivan Hurt, Apr 06 2016 *)

Vec((4*x^4-x^3-x^2-x+3)/((x-1)^2*(x+1)*(x^2+1)) + O(x^90)) \\ Michel Marcus, Apr 06 2016

def a(n): return n^3
print([a(n) for n in range(69)]) # Michael S. Branicky, Jan 23 2022

G.f.: (4*x^4-x^3-x^2-x+3)/((x-1)^2*(x+1)*(x^2+1)). - Ralf Stephan, Nov 01 2003
a(n) = n + (-1)^n + 2*(-1)^floor(n/2). - Mitchell Harris, Jan 10 2005
From Wesley Ivan Hurt, Apr 06 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>4.
a(n) = n + (-1)^n + 2*(-1)^((2*n-1+(-1)^n)/4).
a(n) = A004442(A004443(n)) = A004443(A004442(n)).
a(a(n)) = n; n+a(n) = A004442(n) + A004443(n). (End)
a(n) = n XOR 3. - Falk Hüffner, Jan 23 2022

More terms from Michael S. Branicky, Jan 23 2022

A106449 Square array (P(x) XOR P(y))/gcd(P(x),P(y)) where P(x) and P(y) are polynomials with coefficients in {0,1} given by the binary expansions of x and y, and all calculations are done in polynomial ring GF(2)[X], with the result converted back to a binary number, and then expressed in decimal. Array is symmetric, and is read by antidiagonals.

Original entry on oeis.org

0, 3, 3, 2, 0, 2, 5, 1, 1, 5, 4, 3, 0, 3, 4, 7, 7, 7, 7, 7, 7, 6, 2, 2, 0, 2, 2, 6, 9, 5, 3, 1, 1, 3, 5, 9, 8, 5, 4, 1, 0, 1, 4, 5, 8, 11, 11, 11, 3, 1, 1, 3, 11, 11, 11, 10, 4, 6, 3, 2, 0, 2, 3, 6, 4, 10, 13, 9, 7, 13, 13, 1, 1, 13, 13, 7, 9, 13, 12, 7, 8, 7, 4, 7, 0, 7, 4, 7, 8, 7, 12, 15, 15, 5

Offset: 1

Antti Karttunen, May 21 2005

Array is read by antidiagonals, with row x and column y ranging as: (x,y) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
"Coded in binary" means that a polynomial a(n)*X^n+...+a(0)*X^0 over GF(2) is represented by the binary number a(n)*2^n+...+a(0)*2^0 in Z (where a(k)=0 or 1).
This is GF(2)[X] analog of A106448. In the definition XOR means addition in polynomial ring GF(2)[X], that is, a carryless binary addition, A003987.

			The top left 17 X 17 corner of the array:
        1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17
     +--------------------------------------------------------------------
   1 :  0,  3,  2,  5,  4,  7,  6,  9,  8, 11, 10, 13, 12, 15, 14, 17, 16, ...
   2 :  3,  0,  1,  3,  7,  2,  5,  5, 11,  4,  9,  7, 15,  6, 13,  9, 19, ...
   3 :  2,  1,  0,  7,  2,  3,  4, 11,  6,  7,  8,  5, 14, 13,  4, 19, 14, ...
   4 :  5,  3,  7,  0,  1,  1,  3,  3, 13,  7, 15,  2,  9,  5, 11,  5, 21, ...
   5 :  4,  7,  2,  1,  0,  1,  2, 13,  4,  3, 14,  7,  8, 11,  2, 21,  4, ...
   6 :  7,  2,  3,  1,  1,  0,  1,  7,  5,  2, 13,  3, 11,  4,  7, 11, 13, ...
   7 :  6,  5,  4,  3,  2,  1,  0, 15,  2, 13, 12, 11, 10,  3,  8, 23, 22, ...
   8 :  9,  5, 11,  3, 13,  7, 15,  0,  1,  1,  3,  1,  5,  3,  7,  3, 25, ...
   9 :  8, 11,  6, 13,  4,  5,  2,  1,  0,  1,  2,  3,  4,  1,  2, 25,  8, ...
  10 : 11,  4,  7,  7,  3,  2, 13,  1,  1,  0,  1,  1,  7,  2,  1, 13,  7, ...
  11 : 10,  9,  8, 15, 14, 13, 12,  3,  2,  1,  0,  7,  6,  5,  4, 27, 26, ...
  12 : 13,  7,  5,  2,  7,  3, 11,  1,  3,  1,  7,  0,  1,  1,  1,  7, 11, ...
  13 : 12, 15, 14,  9,  8, 11, 10,  5,  4,  7,  6,  1,  0,  3,  2, 29, 28, ...
  14 : 15,  6, 13,  5, 11,  4,  3,  3,  1,  2,  5,  1,  3,  0,  1, 15, 31, ...
  15 : 14, 13,  4, 11,  2,  7,  8,  7,  2,  1,  4,  1,  2,  1,  0, 31,  2, ...
  16 : 17,  9, 19,  5  21, 11, 23,  3, 25, 13, 27,  7, 29, 15, 31,  0,  1, ...
  17 : 16, 19, 14, 21,  4, 13, 22, 25,  8,  7, 26, 11, 28, 31,  2,  1,  0, ...

Row 1: A004442 (without its initial term), row 2: A106450 (without its initial term).

Cf. A003987, A048720, A091255, A106448, A280500.

up_to = 105;
A106449sq(a,b) = { my(Pa=Pol(binary(a))*Mod(1, 2), Pb=Pol(binary(b))*Mod(1, 2)); fromdigits(Vec(lift((Pa+Pb)/gcd(Pa,Pb))),2); }; \\ Note that XOR is just + in GF(2)[X] world.
A106449list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A106449sq(col,(a-(col-1))))); (v); };
v106449 = A106449list(up_to);
A106449(n) = v106449[n]; \\ Antti Karttunen, Oct 21 2019

A(x, y) = A280500(A003987(x, y), A091255(x, y)), that is, A003987(x, y) = A048720(A(x, y), A091255(x, y)).

A011264 In the prime factorization of n, increment even powers and decrement odd powers (multiplicative).

Original entry on oeis.org

1, 1, 1, 8, 1, 1, 1, 4, 27, 1, 1, 8, 1, 1, 1, 32, 1, 27, 1, 8, 1, 1, 1, 4, 125, 1, 9, 8, 1, 1, 1, 16, 1, 1, 1, 216, 1, 1, 1, 4, 1, 1, 1, 8, 27, 1, 1, 32, 343, 125, 1, 8, 1, 9, 1, 4, 1, 1, 1, 8, 1, 1, 27, 128, 1, 1, 1, 8, 1, 1, 1, 108, 1, 1, 125, 8, 1, 1, 1, 32, 243, 1, 1, 8, 1, 1, 1, 4, 1, 27, 1, 8, 1, 1

Offset: 1

Marc LeBrun

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Cf. A001221, A004442, A007913, A007947, A011262, A027748, A336643, A356191.

a011264 n = product $ zipWith (^)
                      (a027748_row n) (map a004442 $ a124010_row n)
-- Reinhard Zumkeller, Jun 23 2013

f[n_, k_] := n^(If[EvenQ[k], k + 1, k - 1]); Table[Times @@ f @@@ FactorInteger[n], {n, 94}] (* Jayanta Basu, Aug 14 2013 *)

a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^if(f[i,2]%2, f[i,2]-1, f[i,2]+1));} \\ Amiram Eldar, Jan 07 2023

a(n) = Product_{k=1..A001221(n)} (A027748(n,k)^A004442(A124010(n,k))). - Reinhard Zumkeller, Jun 23 2013
From Amiram Eldar, Jan 07 2023: (Start)
a(n) = n^2/A011262(n).
a(n) = n*A007947(n)/A007913(n)^2.
a(n) = n*A336643(n)/A007913(n).
a(n) = A356191(n)/A007913(n). (End)
Dirichlet g.f.: zeta(2*s-2) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-3) - 1/p^(2*s-2)). - Amiram Eldar, Sep 21 2023
From Vaclav Kotesovec, May 06 2025: (Start)
Dirichlet g.f.: zeta(2*s-3) * Product_{p prime} (1 + (p-1)*p^(3-2*s) + p^(1-s) - (p-1)*(p^s + p^3)/(p^(2*s) - p^2)).
Sum_{k=1..n} a(k) ~ n^2/4. (End)

A079354 a(1)=1; a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

Original entry on oeis.org

1, 4, 7, 6, 9, 8, 7, 6, 5, 8, 11, 14, 17, 16, 19, 18, 17, 16, 15, 18, 21, 24, 27, 26, 29, 28, 27, 26, 25, 28, 31, 34, 37, 36, 39, 38, 37, 36, 35, 38, 41, 44, 47, 46, 49, 48, 47, 46, 45, 48, 51, 54, 57, 56, 59, 58, 57, 56, 55, 58, 61, 64, 67, 66, 69, 68, 67, 66, 65, 68, 71, 74, 77

Offset: 1

Benoit Cloitre and N. J. A. Sloane, Feb 14 2003

Starting with a(1)=0 and same definition, a(n)=n+(-1)^n (cf. A004442)

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 2.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{1,4,7,6,9,8,7,6,5,8,11},80] (* Harvey P. Dale, Feb 01 2015 *)

Vec(x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1)/(x^11-x^10-x+1) + O(x^100)) \\ Colin Barker, Oct 16 2013

a(n)-n is periodic with period (0, 2, 4, 2, 4, 2, 0, -2, -4, -2) of length 10.
a(10t+i) = 10t+c_i, 1<=i<=10, c_i=(1, 4, 7, 6, 9, 8, 7, 6, 5, 8). a(n) = n iff n == 1 or 7 (mod 10).
G.f.: x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1) / (x^11-x^10-x+1). - Colin Barker, Oct 16 2013

A080413 Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate left 1 digit.

Original entry on oeis.org

0, 2, 4, 6, 1, 3, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15, 16, 18, 20, 22, 17, 19, 21, 23, 24, 26, 28, 30, 25, 27, 29, 31, 32, 34, 36, 38, 33, 35, 37, 39, 40, 42, 44, 46, 41, 43, 45, 47, 48, 50, 52, 54, 49, 51, 53, 55, 56, 58, 60, 62, 57, 59, 61, 63, 64, 66, 68, 70, 65, 67, 69, 71, 72

Offset: 0

Reinhard Zumkeller, Feb 17 2003

			a(2)=a('010')='100'=4; a(3)=a('011')='110'=6; a(4)=a('100')='001'=1; a(5)=a('101')='011'=3;
a(20)=a('10'100')='10'001'=17; a(21)=a('10'101')='10'011'=19.

Index entries for sequences that are permutations of the natural numbers
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Cf. A007088, A004442, A064429, A080412, A080414.

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 6, 1, 3, 5, 7, 8}, 73] (* Georg Fischer, Jul 03 2025 *)

def A080413(n): return ((n&3)<<1)+bool(n&4)+(n&-8) # Chai Wah Wu, Jan 21 2023

For n>7: a(n) = 8*floor(n/8) + a(n mod 8).
A permutation of natural numbers with inverse = A080414: A080414(a(n))=n, a(A080414(n))=n.
a(a(n))=A080414(n), A080414(A080414(n))=a(n), a(a(a(n)))=n.

A080414 Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate right 1 digit.

Original entry on oeis.org

0, 4, 1, 5, 2, 6, 3, 7, 8, 12, 9, 13, 10, 14, 11, 15, 16, 20, 17, 21, 18, 22, 19, 23, 24, 28, 25, 29, 26, 30, 27, 31, 32, 36, 33, 37, 34, 38, 35, 39, 40, 44, 41, 45, 42, 46, 43, 47, 48, 52, 49, 53, 50, 54, 51, 55, 56, 60, 57, 61, 58, 62, 59, 63, 64, 68, 65, 69, 66, 70, 67, 71, 72

Offset: 0

Reinhard Zumkeller, Feb 17 2003

			a(2)=a('010')='001'=1; a(3)=a('011')='101'=5; a(4)=a('100')='010'=2; a(5)=a('101')='110'=6;
a(20)=a('10'100')='10'010'=18; a(21)=a('10'101')='10'110'=22.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for sequences that are permutations of the natural numbers
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Cf. A007088, A004442, A064429, A080412, A080413.

r3bd[n_]:=Module[{a,b},{a,b}=Reverse[TakeDrop[IntegerDigits[n,2],-3]];FromDigits[Join[a,RotateRight[b]],2]]; Join[{0,4,1,5},Table[r3bd[n],{n,4,80}]] (* Harvey P. Dale, Jul 30 2021 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 4, 1, 5, 2, 6, 3, 7, 8}, 73] (* Georg Fischer, Jul 03 2025 *)

def A080414(n): return ((n&6)>>1)+((n&1)<<2)+(n&-8) # Chai Wah Wu, Jan 21 2023

For n>7: a(n) = 8*floor(n/8) + a(n mod 8).
A permutation of natural numbers with inverse A080413: A080413(a(n))=n, a(A080413(n))=n.
a(a(n))=A080413(n), A080413(A080413(n))=a(n), a(a(a(n)))=n.

A163541 The absolute direction (0=east, 1=south, 2=west, 3=north) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.

Original entry on oeis.org

1, 0, 3, 0, 0, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 0, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 3, 3, 2, 1, 2, 2, 3, 0, 3, 2, 3, 0, 0, 1, 0, 3, 0, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 0, 1, 0, 3, 0, 0, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 1, 0, 3, 0, 0, 1

Offset: 1

Antti Karttunen, Aug 01 2009

nonn

Taking every sixteenth term gives the same sequence: (and similarly for all higher powers of 16 as well): a(n) = a(16*n).

Antti Karttunen, Table of n, a(n) for n = 1..4096

a(n) = A163541(A008598(n)) = A004442(A163540(n)). See also A163543.

HC = {L[n_ /; IntegerQ[n/2]] :> {F[n], L[n], L[n + 1], R[n + 2]},
R[n_ /; IntegerQ[(n + 1)/2]] :> {F[n], R[n], R[n + 3], L[n + 2]},
R[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], F[n + 3]},
L[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], F[n + 1]},
F[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], L[n + 3]},
F[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], R[n + 1]}};
a[1] = L[0]; Map[(a[n_ /; IntegerQ[(n - #)/16]] := Part[Flatten[a[(n + 16 - #)/16]/.HC/.HC],#]) &, Range[16]];
Part[FoldList[Mod[Plus[#1, #2], 4] &, 0, a[#] & /@ Range[4^4]/.{F[n_]:>0,L[n_]:>1,R[n_]:>-1}], 2 ;; -1] (* Bradley Klee, Aug 07 2015 *)

(define (A163541 n) (modulo (+ 3 (A163538 n) (A163539 n) (abs (A163538 n))) 4))

a(n) = A010873(A163538(n) + A163539(n) + abs(A163538(n)) + 3).

A163980 a(n) = 2*n + (-1)^n.

Original entry on oeis.org

1, 5, 5, 9, 9, 13, 13, 17, 17, 21, 21, 25, 25, 29, 29, 33, 33, 37, 37, 41, 41, 45, 45, 49, 49, 53, 53, 57, 57, 61, 61, 65, 65, 69, 69, 73, 73, 77, 77, 81, 81, 85, 85, 89, 89, 93, 93, 97, 97, 101, 101, 105, 105, 109, 109, 113, 113, 117, 117, 121, 121, 125, 125, 129, 129, 133

Offset: 1

Juri-Stepan Gerasimov, Aug 09 2009

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A000027, A004442, A005843, A006752, A033999.

LinearRecurrence[{1, 1, -1}, {1, 5, 5}, 50] (* or *) Table[2*n + (-1)^n, {n,1,50}] (* G. C. Greubel, Aug 24 2017 *)

a(n)=n+n+(-1)^n \\ Charles R Greathouse IV, Jun 09 2011

a(n) = A005843(n) - (-1)^A001477(n).
a(n) = 2*A000027(n) + (-1)^A000027(n).
a(n) = A005843(n) + A033999(n).
From R. J. Mathar, Aug 21 2009: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: x*(1+4*x-x^2)/((1+x)*(1-x)^2). (End)
a(n) = 4*n - 2 - a(n-1), with a(1)=1. - Vincenzo Librandi, Nov 30 2010
E.g.f.: (2*x+1)*cosh(x) +(2*x-1)* sinh(x) -1. - G. C. Greubel, Aug 24 2017
Sum_{n>=1} 1/a(n)^2 = Pi^2/8 + G - 1, where G is Catalan's constant (A006752). - Amiram Eldar, Aug 21 2022

Link by Charles R Greathouse IV, Mar 25 2010

A174239 a(n) = (3n + 1 + (-1)^n(n+3))/4.

Original entry on oeis.org

1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, 19, 9, 21, 10, 23, 11, 25, 12, 27, 13, 29, 14, 31, 15, 33, 16, 35, 17, 37, 18, 39, 19, 41, 20, 43, 21, 45, 22, 47, 23, 49, 24, 51, 25, 53, 26, 55, 27, 57, 28, 59, 29, 61, 30, 63, 31, 65, 32, 67, 33, 69, 34, 71, 35, 73, 36, 75, 37, 77, 38, 79, 39, 81

Offset: 0

Paul Curtz, Mar 13 2010

Obtained from A026741 by swapping pairs of consecutive entries.
The main diagonal of an array with this sequence in the top row and further rows defined by the first differences of their previous row is essentially 1 followed by 3*A045623(.):
1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, ...
-1, 3, -2, 4, -3, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, ...
4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, ...
-9, 11, -13, 15, -17, 19, -21, 23, -25, 27, -29, 31, ...
20, -24, 28, -32, 36, -40, 44, -48, 52, -56, 60, -64, ...
-44, 52, -60, 68, -76, 84, -92, 100, -108, 116, -124, 132, ...
96, -112, 128, -144, 160, -176, 192, -208, 224, -240, ...
Also, numerator of (Nimsum n+1)/2 = A004442(n)/2. - Wesley Ivan Hurt, Mar 21 2015

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A004442.

[(3*n+1 +(-1)^n*(n+3))/4: n in [0..80]]; // Vincenzo Librandi, Feb 08 2011

A174239:=n->(3*n+1+(-1)^n*(n+3))/4: seq(A174239(n), n=0..100); # Wesley Ivan Hurt, Mar 21 2015

Table[(3 n + 1 + (-1)^n*(n + 3))/4, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 21 2015 *)
LinearRecurrence[{0,2,0,-1},{1,0,3,1},90] (* Harvey P. Dale, Jul 16 2018 *)

a(2n) = 2n+1; a(2n+1) = n.
a(n) = 2*a(n-2) - a(n-4).
a(2n+1) - 2*a(2n) = -A016789(n+1).
a(2n+2) - 2*a(2n+1) = 3.
G.f.: ( 1+x^2+x^3 ) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Feb 07 2011

A261098 Row 1 of A261096.

Original entry on oeis.org

1, 0, 4, 5, 2, 3, 7, 6, 10, 11, 8, 9, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 25, 24, 28, 29, 26, 27, 31, 30, 34, 35, 32, 33, 42, 43, 44, 45, 46, 47, 36, 37, 38, 39, 40, 41, 49, 48, 52, 53, 50, 51, 55, 54, 58, 59, 56, 57, 66, 67, 68, 69, 70, 71, 60, 61, 62, 63, 64, 65, 96, 97, 98, 99, 100, 101

Offset: 0

Antti Karttunen, Aug 26 2015

nonn

Equally, column 1 of A261097.
Take the n-th (n>=0) permutation from the list A055089 (A195663), change 1 to 2 and 2 to 1 to get another permutation, and note its rank in the same list to obtain a(n).
Self-inverse permutation of nonnegative integers.

			In A195663 the permutation with rank 12 is [1,3,4,2], and swapping the elements 1 and 2 we get permutation [2,3,4,1], which is listed in A195663 as the permutation with rank 18, thus a(12) = 18.

Antti Karttunen, Table of n, a(n) for n = 0..5039
Index entries for sequences that are permutations of the natural numbers

Row 1 of A261096, column 1 of A261097.
Cf. A055089, A195663.
Cf. also A004442.
Related permutations: A060119, A060126, A261218.

a(n) = A261096(1,n).
By conjugating related permutations:
a(n) = A060119(A261218(A060126(n))).

cp's OEIS Frontend

A004444 Nimsum n + 3.

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A011264 In the prime factorization of n, increment even powers and decrement odd powers (multiplicative).

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A079354 a(1)=1; a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

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A080413 Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate left 1 digit.

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A080414 Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate right 1 digit.

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A163541 The absolute direction (0=east, 1=south, 2=west, 3=north) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.

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A174239 a(n) = (3n + 1 + (-1)^n(n+3))/4.