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

Author

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

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..5000
• Index entries related to non-averaging sequences

Crossrefs

Cf. A101885, A101886, A101888. Also A094870.

Programs

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