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URL: https://oeis.org/A224853

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A224853
Lexicographically earliest sequence of nonnegative integers which does not contain a three-term 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
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
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
KEYWORD
nonn,look
AUTHOR
Timur Vural, Jul 28 2013
STATUS
approved