A080458 -id:A080458 - cp's OEIS frontend

A080199 a(1)=1; for n>1, a(n)=a(n-1) - 3 if n is already in the sequence, a(n)=a(n-1) + 6 otherwise.

1, 7, 13, 19, 25, 31, 28, 34, 40, 46, 52, 58, 55, 61, 67, 73, 79, 85, 82, 88, 94, 100, 106, 112, 109, 115, 121, 118, 124, 130, 127, 133, 139, 136, 142, 148, 154, 160, 166, 163, 169, 175, 181, 187, 193, 190, 196, 202, 208, 214, 220, 217, 223, 229

Offset: 1

N. J. A. Sloane, Mar 20 2003

nonn

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Cf. A080455-A080458, A080036, A080037.

a[1] = 1;
a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]-3, a[n-1]+6];
Array[a, 54] (* Jean-François Alcover, Feb 13 2019 *)

a(n) = 3*n*(1 + 1/log_3(n)) + o(n).

A080460 a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.

Original entry on oeis.org

2, 2, 6, 10, 14, 14, 18, 22, 26, 26, 30, 34, 38, 38, 42, 46, 50, 50, 54, 58, 62, 62, 66, 70, 74, 74, 78, 82, 86, 86, 90, 94, 98, 98, 102, 106, 110, 110, 114, 118, 122, 122, 126, 130, 134, 134, 138, 142, 146, 146, 150, 154, 158, 158, 162, 166, 170, 170

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Mar 22 2003

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Cf. A080455, A080456, A080457, A080458, A080036, A080037.

LinearRecurrence[{1, 0, 0, 1, -1}, {2, 2, 6, 10, 14}, 58] (* Jean-François Alcover, Jan 07 2019 *)

a(n)=4*n - (n-2)\4*4 - 6 \\ Charles R Greathouse IV, Jul 17 2016

a(n) = 2 + 4*(n - 2 - floor((n - 2)/4)).
From Chai Wah Wu, Jul 17 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
G.f.: 2*x*(x^4 + 2*x^3 + 2*x^2 + 1)/(x^5 - x^4 - x + 1). (End)
From Ilya Gutkovskiy, Jul 17 2016: (Start)
E.g.f.: 2 + (3*x - 2)*sinh(x) + 3*(x - 1)*cosh(x) + sin(x) + cos(x).
a(n) = (6*n - (-1)^n + 2*sqrt(2)*sin(Pi*n/2 + Pi/4) - 5)/2. (End)

A126091 a(1)=1;a(2)=4; for n>2, a(n)=a(n-2)+3 if n is already in the sequence, a(n)=a(n-2)+1 otherwise.

Original entry on oeis.org

1, 4, 2, 7, 3, 8, 6, 11, 7, 12, 10, 15, 11, 16, 14, 19, 15, 20, 18, 23, 19, 24, 22, 27, 23, 28, 26, 31, 27, 32, 30, 35, 31, 36, 34, 39, 35, 40, 38, 43, 39, 44, 42, 47, 43, 48, 46, 51, 47, 52, 50, 55, 51, 56, 54, 59, 55, 60, 58, 63, 59, 64, 62, 67, 63, 68, 66, 71, 67, 72, 70, 75

Offset: 1

Zak Seidov, Mar 11 2007

nonn

Cf. A080578, A080455-A080458.

a={1,4};Do[If[MemberQ[a,n],b=a[[n-2]]+3,b=a[[n-2]]+1];AppendTo[a,b],{n,3,70}];a

cp's OEIS Frontend

A080199 a(1)=1; for n>1, a(n)=a(n-1) - 3 if n is already in the sequence, a(n)=a(n-1) + 6 otherwise.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A080460 a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A126091 a(1)=1;a(2)=4; for n>2, a(n)=a(n-2)+3 if n is already in the sequence, a(n)=a(n-2)+1 otherwise.

Views

Author

Keywords

Crossrefs

Programs

Mathematica