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%I #32 Jan 16 2020 08:07:25
%S 0,3,1,5,10,19,15,22,31,51,61,37,82,71,126,96,92,136,162,187,206,276,
%T 191,261,236,247,317,302,401,292,422,547,456,544,551,612,591,577,521,
%U 666,742,726,682,877,796,1052,961,1046,1171,1027,954,1017,1006,1207,1396,1262,1311,1496,1482,1571,1717
%N Smallest nonnegative number k such that A240088(k) = n.
%H Giovanni Resta, <a href="/A275999/b275999.txt">Table of n, a(n) for n = 1..10000</a> (first 1007 terms from Robert G. Wilson v)
%e a(1) = 0 since A240088(0) = 1, namely 0+0+0;
%e a(2) = 3 since A240088(3) = 2, namely 1+1+1 or 3+0+0;
%e a(3) = 1 since A240088(1) = 3, namely 1+0+0 or 0+1+0 or 0+0+1;
%e with triangular number followed by square number followed by pentagonal number.
%t f[n_] := Block[{c = pi = 0, pn, plmt = Floor[(Sqrt[1 + 24 n] + 7)/6], ti, tlmt}, While[pi < plmt, ti = 0; pn = pi (3pi -1)/2; tlmt = Floor[(Sqrt[1 +8(n - pn)] + 1)/2] +1; While[ti < tlmt, If[IntegerQ[Sqrt[n - pn - ti (ti + 1)/2]], c++]; ti++]; pi++]; c]; t = 0*Range@ 1000; k = 0; While[k < 100001, a = f@ k; If[ t[[a]] == 0, t[[a]] = k]; k++]; t
%Y Cf. A240088.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Aug 17 2016
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