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

Author

Timur Vural, Jul 28 2013

Keywords

• nonn
• look

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A225571, A003278, A005836, A000452.

Programs

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