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A225385 Construct sequences P,Q,R by the rules: Q = first differences of P, R = second differences of P, P starts with 1,3,9, Q starts with 2,6, R starts with 4; at each stage the smallest number not yet present in P,Q,R is appended to R. Sequence gives P. 4
1, 3, 9, 20, 38, 64, 100, 148, 209, 284, 374, 480, 603, 745, 908, 1093, 1301, 1533, 1790, 2074, 2386, 2727, 3098, 3500, 3934, 4401, 4902, 5438, 6011, 6623, 7275, 7968, 8703, 9481, 10303, 11170, 12083, 13043, 14052, 15111, 16221, 17383, 18598, 19867, 21191, 22571, 24008, 25503, 27057, 28671, 30347, 32086, 33890, 35760, 37697, 39702, 41776, 43920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In contrast to A225376-A225378, here it is not required (and not true) that each number should appear just once in P union Q union R. On the other hand, again in contrast to A225376-A225378, here it is obvious that P, Q, R are infinite.

The first three numbers that are repeated are 284, 2074, 3500, which appear in both P and Q. There may be no others. Of course R is disjoint from P and Q, by definition.

LINKS

Table of n, a(n) for n=1..58.

MAPLE

# Based on Christopher Carl Heckman's program for A225376.

f:=proc(N) local h, dh, ddh, S, mex, i;

h:=1, 3, 9; dh:=2, 6; ddh:=4; mex:=5; S:={h, dh, ddh};

for i from 4 to N do

while mex in S do S:=S minus {mex}; mex:=mex+1; od;

ddh:=ddh, mex; dh:=dh, dh[-1]+mex; h:=h, h[-1]+dh[-1];

S:=S union {h[-1], dh[-1], ddh[-1]};

mex:=mex+1;

od;

RETURN([[h], [dh], [ddh]]);

end;

f(100);

CROSSREFS

Cf. A225386, A225387, A005228, A030124, A037257, A225376, A225377, A225378.

Sequence in context: A187409 A037048 A139142 * A037257 A145068 A293357

Adjacent sequences:  A225382 A225383 A225384 * A225386 A225387 A225388

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 15 2013

STATUS

approved

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)