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A381619 Sorted list of sums of 3 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.

%I A381619 #15 Jun 05 2025 13:55:16
%S A381619 525,540,546,549,555,561,567,570,585,588,600,612,630,642,660,660,663,
%T A381619 675,726,735,744,750,759,765,783,792,798,810,819,825,840,840,891,897,
%U A381619 900,930,945,957,966,966,975,981,996,1050,1050,1071,1080,1092,1125,1134,1155,1155,1170
%N A381619 Sorted list of sums of 3 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.
%C A381619 The sequence has 622 terms. See linked files for all solutions.
%C A381619 A natural number s occurs k times in the list if there exist k multisets {x,y,z} of natural numbers with s = x + y + z and 10000*s = x*y*z.
%H A381619 Hugo Pfoertner, <a href="/A381619/b381619.txt">Table of n, a(n) for n = 1..622</a>
%H A381619 Hugo Pfoertner, <a href="/A381619/a381619.txt">Solution triples sorted by sum</a>. (2025)
%H A381619 Hugo Pfoertner, <a href="/A381619/a381619_1.txt">Solution triples sorted by smallest price</a>. (2025)
%H A381619 Eric Snyder and others, <a href="https://math.stackexchange.com/questions/4482769/">Finding solutions of sum a_i = product a_i = n</a>, where the a_i are "price rationals", question in Mathematics StackExchange, Jun 29, 2022.
%e A381619 a(1) = 525 because 1.50 + 1.75 + 2.00 = 1.50*1.75*2.00 = 5.25 is the solution with minimum sum;
%e A381619 a(15) = a(16) = 660 because there are 2 solutions:
%e A381619   0.80 + 2.50 + 3.30 = 0.80*2.50*3.30 = 6.60 and
%e A381619   1.10 + 1.50 + 4.00 = 1.10*1.50*4.00 = 6.60;
%e A381619 a(31) = a(32) = 840:
%e A381619   0.60 + 2.80 + 5.00 = 0.60*2.80*5.00 = 8.40 and
%e A381619   1.00 + 1.40 + 6.00 = 1.00*1.40*6.00 = 8.40;
%e A381619 a(622) = 100030002 is the largest term:
%e A381619   0.01 + 100.01 + 1000200.00 = 0.01*100.01*1000200.00 = 1000300.02.
%Y A381619 Cf. A380887, A381187, A381620, A381621, A382510.
%K A381619 nonn,base,fini,full
%O A381619 1,1
%A A381619 _Hugo Pfoertner_ and _Markus Sigg_, Mar 02 2025