A080591 -id:A080591 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 23 2003

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.

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.

Cf. A079000, A080591, A080589.

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

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

A102046 Smallest positive integer greater than a(n - 1) consistent with the condition that n is a member of the sequence if and only if a(n) is congruent to (n!)!.

Original entry on oeis.org

1, 1, 2, 6, 7, 8, 720, 721, 722, 723, 724, 726, 727, 728, 729, 780, 781, 782, 783, 784, 785, 786, 787, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799

Offset: 0

Michael Joseph Halm, Feb 12 2005

The sequence is related to the fake even and fake odd sequences and also the factorial and double factorial sequences, so seems in the short run linear but in the long run exponential.

			a(6) = 720 because (3!)! = 6! = 720

Cf. A080591, A080588, A000197, A000142.

a(a(n)) = (n!)!

The definition does not match the data. How was this sequence generated? - N. J. A. Sloane, Feb 21 2021

cp's OEIS Frontend

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

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