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%I #29 Jun 22 2019 10:45:59
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100
%N Sums of no more than two 5-smooth numbers.
%C Sequence includes 5-smooth numbers (A051037).
%C Numbers that are of the form (2^i * 3^j * 5^k)*a + (2^m * 3^n * 5^p)*b, with i,j,k,m,n,p >= 0, and a,b = 0 or 1. The first number excluded is 71. The numbers excluded are in A323049.
%e 70 = 2*2*3*5 + 2*5, 72 = 2*2*2*3*3 = 2*2*3*5 + 2*2*3, but 71 is not in the sequence.
%t S5 = Join[{0}, Select[Range[500], FactorInteger[#][[-1, 1]] <= 5 &]];
%t Union@Flatten@Outer[Plus, S5, S5]
%t (* more efficient code by _Michael De Vlieger_ *)
%t f[n_] := Union@Flatten@Table[2^a*3^b*5^c, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a*3^b)]}]; Block[{nn = 500, s}, s = f[nn]; {0, 1}~Join~
%t Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]]
%Y Cf. A051037, A323049 (complementary sequence).
%K nonn
%O 1,3
%A _Carlos Alves_, Jan 03 2019
%E Name edited by _Jianing Song_, Jun 11 2019
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