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%I #15 Nov 01 2014 13:08:41
%S 0,2,12,30,56,90,143,210,272,342,420,506,600,702,812,992,1122,1260,
%T 1406,1560,1722,1892,2070,2256,2450,2652,2862,3135,3422,3660,3906,
%U 4160,4422,4692,4970,5256,5550,5852,6162,6480,6806,7140,7482,7832,8372,8742,9120,9506,9900
%N a(1)=0; the next term is always the product of the two smallest numbers not yet in the sequence and which have not yet been used.
%C Suggested by A075336 and A249406.
%e Start with a(1) = 0. The missing numbers are 1 2 3 4 5 6 ...
%e Multiply the first two, and we get 2, which is therefore a(2).
%e Cross 1, 2, and 1*2 = 2 off the missing list.
%e The first two missing numbers are now 3 and 4, so a(3) = 3*4 = 12.
%e Cross off 3,4,12 from the missing list.
%e Repeat!
%p M:=50; A:=[0]; miss:=[seq(n,n=1..M^2)]:
%p for n from 1 to M do t1:=miss[1]*miss[2]; A:=[op(A),t1];
%p miss:=[seq(miss[i],i=3..nops(miss))];
%p miss:=remove('x->x=t1',miss);
%p od:
%p A;
%Y Cf. A075326, A000045, A249406, A000304, A000301.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 01 2014
%E Typo in definition corrected by _Douglas Latimer_, Nov 01 2014
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