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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
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
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: A367295 A212905 A191117 * A320693 A274848 A201020
KEYWORD
nonn
AUTHOR
Peter Kagey, Dec 08 2015
STATUS
approved