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 A265389 The sums from the following procedure: from the list of positive integers, repeatedly remove the first three numbers and their sum. 11
 6, 16, 27, 36, 46, 57, 66, 75, 87, 96, 106, 117, 126, 136, 147, 156, 165, 177, 186, 196, 207, 216, 227, 237, 246, 255, 267, 276, 286, 297, 306, 316, 327, 336, 345, 357, 366, 376, 387, 396, 406, 417, 426, 435, 447, 456, 466, 477, 486, 497, 507, 516, 525, 537 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a solution, along with three other sequences, of a system of four complementary equations; see A297464.  It is the "anti-tribonacci" sequence, in analogy with the anti-Fibonacci sequence, A075326. - Clark Kimberling, Apr 22 2018 LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 William Lowell Putnam Competition, Problem B2, 2015. MAPLE S:= {\$1..1000}: A:= NULL: while nops(S) >= 3 do   T:= S[1..3];   s:= convert(T, `+`);   S:= S[4..-1] minus {s};   A:= A, s od: A; # Robert Israel, Dec 22 2015 MATHEMATICA f[n_] := Block[{a = {}, r = Range@ n, s}, Do[If[Length@ r > 4, s = Total@ Take[r, 3 ]; AppendTo[a, s]; r = Drop[#, 3] &@ DeleteCases[r, x_ /; x == s], Break[]], {k, n}]; a]; f@ 184 (* Michael De Vlieger, Dec 22 2015 *) morph = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0}, 2 -> {1, 0, 0}}] &, {0}, 9]; A265389 = Accumulate[Prepend[Drop[Flatten[morph /. Thread[{0, 1, 2} -> {{1, 1, 4}, {1, 2, 3}, {1, 3, 2}}]], 1] + 8, 6]]; Take[A265389, 100]    (* Peter J. C. Moses, May 03 2018 *) PROG (Ruby) x = (1..10000).to_a (0...1000).collect do   y = x.shift(3).reduce(:+); x.delete_at x.index(y); y end CROSSREFS Sequence in context: A222180 A212905 A191117 * A320693 A274848 A201020 Adjacent sequences:  A265386 A265387 A265388 * A265390 A265391 A265392 KEYWORD nonn AUTHOR Peter Kagey, Dec 08 2015 STATUS approved

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Last modified May 21 09:15 EDT 2019. Contains 323441 sequences. (Running on oeis4.)