

A080653


a(1) = 2; for n>1, a(n) is taken to be the smallest integer greater than a(n1) such that the condition "a(a(n)) is always even" is satisfied.


7



2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 95, 96, 97
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OFFSET

1,1


COMMENTS

Also defined by: a(n) = smallest positive number > a(n1) such that the condition "n is in sequence if and only if a(n) is odd" is false (cf. A079000); that is, the condition "either n is not in the sequence and a(n) is odd or n is in the sequence and a(n) is even" is satisfied.
If prefixed with a(0) = 0, can be defined by: a(n) = smallest nonnegative number > a(n1) such that the condition "n is in sequence only if a(n) is even" is satisfied.


REFERENCES

HsienKuei 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/wpcontent/files/2016/12/aathhrr1.pdf. Also Exact and Asymptotic Solutions of a DivideandConquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585


LINKS

Yifan Xie, 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 (math.NT/0305308)


FORMULA

a(a(n) = 2*n+2.  Yifan Xie, Jul 14 2022


MATHEMATICA

(* b = A007378 *) b[n_] := b[n] = Which[n == 2, 3, n == 3, 4, EvenQ[n], 2 b[n/2], True, b[(n1)/2+1]+b[(n1)/2]]; a[1] = 2; a[n_] := b[n+2]2; Table[a[n], {n, 1, 65}] (* JeanFrançois Alcover, Oct 05 2016 *)


CROSSREFS

Equals A007378  2.
A007378, A079905, A080637, A080653 are all essentially the same sequence.
Cf. A169956, A169957.
Sequence in context: A169956 A342495 A035500 * A115836 A176554 A284895
Adjacent sequences: A080650 A080651 A080652 * A080654 A080655 A080656


KEYWORD

easy,nonn,nice


AUTHOR

Matthew Vandermast, Mar 01 2003


STATUS

approved



