A101884 Smallest increasing natural number sequence without any length 3 equidistant arithmetic subsequences.

1, 2, 4, 5, 8, 9, 11, 12, 16, 18, 19, 21, 26, 28, 29, 32, 33, 35, 36, 39, 43, 44, 46, 47, 54, 56, 59, 60, 62, 63, 68, 69, 71, 72, 80, 82, 86, 88, 91, 93, 94, 99, 103, 106, 113, 115, 116, 120, 122, 127, 130, 131, 133, 134, 137, 141, 142, 144, 145, 149, 154

Offset

1,2

Comments

If the restriction "increasing" is removed sequence A094870 is obtained.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Index entries related to non-averaging sequences

Example

3 is out because of 1,2,3. 7 is out because of 1,4,7.
8 is allowed even though 2,5,8 appears in the sequence, because 2, 5, and 8 are not spaced equidistant within the sequence.

Maple

lim:=61: a[1]:=1:a[2]:=2: for n from 3 to lim do na := {}: for j from 1 to floor((n-1)/2) do na := na union {2*a[n-j]-a[n-2*j]}: od: for j from a[n-1]+1 do if(not member(j, na))then a[n]:=j:break: fi: od:od: seq(a[n], n=1..lim); # Nathaniel Johnston, Jun 16 2011

Crossrefs

Cf. A101885, A101886, A101888. Also A094870.

Sequence in context: A288214 A117121 A101925 * A118179 A096603 A084464

Adjacent sequences: A101881 A101882 A101883 * A101885 A101886 A101887

Keyword

nonn,easy

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 20 2004

Status

approved