

A079905


a(1)=1; then a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n+1 for n>1.


7



1, 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
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OFFSET

1,2


COMMENTS

Alternate definition: a(n) is taken to be smallest positive integer greater than a(n1) such that the condition "a(a(n)) is always odd" can be satisfied.  Matthew Vandermast, Mar 03 2003
Also: a(n)=smallest positive integer > a(n1) such that the condition "n is in the sequence if and only if a(n) is even" is false; 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.  Matthew Vandermast, Mar 05 2003


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

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(1)=1, a(2)=3, then a(3*2^k  1 + j) = 4*2^k  1 + 3j/2 + j/2 for k >= 1, 2^k <= j < 2^k.
a(n) = 1+A079945(n1)A079944(n1) for n>1, a(1)=1.  Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003


MATHEMATICA

b[n_] := b[n] = If[n<4, n+1, If[OddQ[n], b[(n1)/2+1]+b[(n1)/2], 2b[n/2]]];
a[n_] := If[n == 1, 1, b[n+1]  1];
a /@ Range[70] (* JeanFrançois Alcover, Oct 18 2019, after Vladeta Jovovic in A007378 *)


CROSSREFS

See A080637 for a nicer version. Cf. A079000.
Equals A007378(n+1)1, n>1.
A007378, A079905, A080637, A080653 are all essentially the same sequence.
Cf. A169956, A169957.
Sequence in context: A285510 A174415 A103826 * A321321 A154611 A189669
Adjacent sequences: A079902 A079903 A079904 * A079906 A079907 A079908


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Feb 21 2003


EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003


STATUS

approved



