

A224853


Lexicographically earliest sequence of nonnegative integers which does not contain a threeterm arithmetic, geometric, or harmonic subsequence.


3



0, 1, 3, 4, 10, 11, 13, 14, 29, 30, 32, 33, 38, 39, 41, 42, 85, 86, 88, 89, 94, 95, 97, 98, 112, 113, 115, 116, 122, 123, 125, 238, 248, 251, 252, 255, 257, 260, 261, 273, 275, 278, 279, 287, 288, 292, 330, 331, 334, 335
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

This sequence diverges from A225571 at 477th term. Here a(477) = 17408, while A225571(477) = 17380.  Giovanni Resta, Jul 29 2013


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


EXAMPLE

After terms 0, 1, 3, 4 have been added, the terms 5,...,9 are forbidden by subsequences (3,4,5), (0,3,6), (1,4,7), (0,4,8) and (1,3,9) so the next term is 10.


PROG

Python Program that generates all values of a(x) less than a given input n.
def a(n):
......seq=[0, 1]
......for x in range(2, n+1):
..........c=0
..........for y in seq:
..............if (x+y)/2 not in seq:
..................if (x*y)**0.5 not in seq[1:]:
......................if (2*x*y)/(x+y) not in seq[1:]:
..........................c+=1
..........if c==len(seq):
..............seq.append(x)
......return seq


CROSSREFS

Cf. A225571, A003278, A005836, A000452.
Sequence in context: A292564 A191192 A139063 * A225571 A191134 A196101
Adjacent sequences: A224850 A224851 A224852 * A224854 A224855 A224856


KEYWORD

nonn,look


AUTHOR

Timur Vural, Jul 28 2013


STATUS

approved



