A224853 Lexicographically earliest sequence of nonnegative integers which does not contain a three-term arithmetic, geometric, or harmonic subsequence.

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

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