

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
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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 "antitribonacci" sequence, in analogy with the antiFibonacci 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



