A079948 First differences of A079000.

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

Offset

1,1

Comments

Alternate description of sequence: start with a(1)=3; apply 1->2, 2->11, 3->21; iterate. - Matthew Vandermast, Mar 08 2003

References

N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.

Links

Table of n, a(n) for n=1..105.

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.

N. J. A. Sloane, Seven Staggering Sequences.

Formula

After first two terms, a run of length 3*2^k 1's followed by a run of length 3*2^k 2's, for k = 0, 1, ...

a(n) = floor(log_2(8*(floor((n+3)/3))/3)) - floor(log_2(floor((n+3)/3))) for n>2; with a(1)=3 and a(2)=2. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 22 2003

Also a(n) = A079882(A002264(n+3)) for n>2, where A002264=floor(n/3). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 22 2003

Mathematica

b[1] = 1; b[n_] := (k = Floor[Log[2, (n+3)/6]]; j = n - (9*2^k-3); 12*2^k - 3 + 3*j/2 + Abs[j]/2); Array[b, 106] // Differences (* Jean-François Alcover, Sep 02 2018 *)

Crossrefs

Sequence in context: A072115 A210650 A218754 * A257657 A339584 A106689

Adjacent sequences: A079945 A079946 A079947 * A079949 A079950 A079951

Keyword

nonn

Author

N. J. A. Sloane, Feb 22 2003

Status

approved