A080645 a(1) = 1; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition "for n>1, if n is a member of the sequence then a(n) is even".

1, 2, 4, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107

Offset

1,2

References

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

Links

Table of n, a(n) for n=1..75.

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)

Index entries for sequences of the a(a(n)) = 2n family

Formula

a(1)=1, a(2)=2, a(3)=4; then for k>=1, abs(j)<=2^k: a(3*2^k+j)=4*2^k+3/2*j+abs(j)/2.

{a(a(n))} = {1, 2, 2i, i >= 3}.

Crossrefs

Cf. A080639, A080640, A079000.

Essentially the same as A007378.

Sequence in context: A216345 A026510 A138204 * A024413 A153347 A330945

Adjacent sequences: A080642 A080643 A080644 * A080646 A080647 A080648

Keyword

nonn,easy

Author

N. J. A. Sloane and Benoit Cloitre, Feb 28 2003

Status

approved