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
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
Programs
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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
Comments