This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A240555 Lexicographically earliest positive increasing sequence such that no four terms have constant second differences. 12
 1, 2, 3, 5, 6, 9, 16, 17, 18, 21, 45, 52, 53, 54, 57, 59, 65, 79, 167, 168, 193, 196, 197, 201, 203, 204, 207, 218, 227, 249, 250, 277, 313, 650, 658, 679, 682, 683, 716, 727, 741, 744, 748, 751, 772, 791, 831, 834, 837, 839, 843, 855, 876, 909, 912, 972 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If "positive" is changed to "nonnegative" we get A240075, which is this sequence minus 1. See A005837 for the earliest sequence containing no 4-term arithmetic progression. 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( #v1, ); #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): 3-term AP: A005836 (>=0), A003278 (>0); 4-term AP: A005839 (>=0), A005837 (>0); 5-term AP: A020654 (>=0), A020655 (>0); 6-term AP: A020656 (>=0), A005838 (>0); 7-term AP: A020657 (>=0), A020658 (>0); 8-term AP: A020659 (>=0), A020660 (>0); 9-term AP: A020661 (>=0), A020662 (>0); 10-term AP: A020663 (>=0), A020664 (>0). Cf. A240075 (nonnegative version, a(n)-1). Cf. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences. Sequence in context: A294631 A059454 A138538 * A102694 A124253 A256230 Adjacent sequences:  A240552 A240553 A240554 * A240556 A240557 A240558 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 12:12 EDT 2019. Contains 328056 sequences. (Running on oeis4.)