OFFSET
1,2
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 1..755 (terms < 10^6)
EXAMPLE
After 1,2,3 the number 4 is excluded since (1,2,3,4) has zero second and third differences.
After 1,2,3,5 the number 8 is excluded since (2,3,5,8) has second differences 1,1.
MATHEMATICA
t = {1, 2, 3}; Do[s = Table[Append[i, n], {i, Subsets[t, {3}]}]; If[! MemberQ[Flatten[Table[Differences[i, 3], {i, s}]], 0], AppendTo[t, n]], {n, 4, 1000}]; t
PROG
(PARI) A240555(n, show=0, L=4, o=2, v=[1], D=v->v[2..-1]-v[1..-2])={ my(d, m); while( #v<n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while( v[#v]++, forvec( i=vector(L, j, [if(j<L, j, #v), #v]), d=D(vecextract(v, i)); m=o; while(m--&&#Set(d=D(d))>1, ); #Set(d)>1||next(2), 2); break)); v[#v]} \\ M. F. Hasler, Jan 12 2016
CROSSREFS
Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
Cf. A240075 (nonnegative version, a(n)-1).
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 09 2014
EXTENSIONS
Definition corrected by N. J. A. Sloane, Jan 04 2016 and M. F. Hasler at the suggestion of Lewis Chen
STATUS
approved