A080588 a(n) is the smallest nonnegative integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 4n.

0, 2, 4, 5, 8, 12, 13, 14, 16, 17, 18, 19, 20, 24, 28, 29, 32, 36, 40, 44, 48, 49, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 84, 88, 92, 96, 100, 104, 108, 112, 113, 114, 115, 116, 120, 124, 125

Offset: 0

Author

N. J. A. Sloane, Feb 23 2003

Keywords

• nonn
• easy
• nice

Comments

Equivalently: a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 4".

The sequence of even numbers shares many of the properties of this sequence.

Links

• Mathieu Gouttenoire, Table of n, a(n) for n = 0..100000
• J.-P. Allouche, N. Rampersad, and Jeffrey Shallit, On integer sequences whose first iterates are linear, Aequationes Math. 69 (2005), 114-127.
• Benoit Cloitre, N. J. A. Sloane, and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
• Benoit Cloitre, N. J. A. Sloane, and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
• Index entries for sequences of the a(a(n)) = 2n family.

Crossrefs

Cf. A079000, A080591, A080589.

Formula

a(a(n)) = 4n. a(2^k) = 2^(k+1).

a(n) = A080591(n-1) + 1, n >= 1.