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%I #9 Jan 24 2018 08:47:42
%S 1,3,8,11,19,25,32,38,42,53,64,75,101,124,147,163,179,195,289,296,299,
%T 315,352,368,384,720,736,752,768,912,980,1034,1066,1098,2100,2132,
%U 2164,2196,2289,2382
%N a(1) = 1, a(2) = 3, for n >= 3; a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + h] * [a(n-1) + h]] / [a(n-2) + a(n-1) + h] is integer.
%H G. C. Greubel, <a href="/A182759/b182759.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 5; a(3) = 8, a(4) = 11, a(5) = 19 before [(8+11)*(8+19)*(11+19)] / (8+11+19) = 405 (integer).
%t nxt[{a_, b_}]:= Module[{h = b + 1}, While[! IntegerQ[((a + b) (a + h) (b + h))/(a + b + h)], h++]; {b, h}]; Transpose[NestList[nxt, {1, 3}, 100]][[1]] (* _G. C. Greubel_, Jan 23 2018 *)
%Y Cf. A182758.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Nov 28 2010
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