A080574 - OEIS

A080574

a(1)=1, a(n)=a(n-1)+1 if n is odd and already in the sequence, a(n)=a(n-1)+2 if n is even and already in the sequence, a(n)=a(n-1)+3 otherwise.

1, 4, 7, 9, 12, 15, 16, 19, 20, 23, 26, 28, 31, 34, 35, 37, 40, 43, 44, 46, 49, 52, 53, 56, 59, 61, 64, 66, 69, 72, 73, 76, 79, 81, 82, 85, 86, 89, 92, 94, 97, 100, 101, 103, 106, 108, 111, 114, 115, 118, 121, 123, 124, 127, 130, 132, 135, 138, 139, 142

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

FORMULA

It appears that a(n) is asymptotic to c*n where c=2.36... is the largest root of q^2-3*q+3/2 = 0.

MATHEMATICA

a[1] = 1;

a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], If[OddQ[n], a[n-1]+1, a[n-1]+2], a[n-1]+3];

Array[a, 60] (* Jean-François Alcover, Feb 13 2019 *)

CROSSREFS

Sequence in context: A279054 A086824 A266936 * A189367 A310951 A310952

Adjacent sequences: A080571 A080572 A080573 * A080575 A080576 A080577

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Mar 23 2003

STATUS

approved