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A080637 a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(1)=2, a(a(n)) = 2n+1 for n>1. 5
2, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 96, 97, 98, 99, 100, 101, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is unique monotonic sequence satisfying a(1)=2, a(a(n)) = 2n+1 for n>1.

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..70.

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(3*2^k - 1 + j) = 4*2^k - 1 + 3j/2 + |j|/2 for k >= 0, -2^k <= j < 2^k.

a(2n+1) = 2*a(n) + 1, a(2n) = a(n) + a(n-1) + 1.

MAPLE

t := []; for k from 0 to 6 do for j from -2^k to 2^k-1 do t := [op(t), 4*2^k - 1 + 3*j/2 + abs(j)/2]; od: od: t;

CROSSREFS

Except for first term, same as A079905. Cf. A079000.

A007378, A079905, A080637, A080653 are all essentially the same sequence.

Equals A007378(n+1)-1. First differences give A079882.

Sequence in context: A299785 A018559 A057196 * A124134 A007071 A242482

Adjacent sequences:  A080634 A080635 A080636 * A080638 A080639 A080640

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)