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A384795 Sorted list of sums of 5 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 A384795 #12 Jun 22 2025 00:51:43
%S A384795 759,760,762,765,770,770,774,777,779,780,780,780,783,783,784,785,786,
%T A384795 791,791,792,792,792,795,798,798,798,798,798,799,799,800,804,804,805,
%U A384795 805,805,806,808,810,810,810,810,810,810,810,810,812,812,813,816,816,816,817,817,817
%N A384795 Sorted list of sums of 5 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 A384795 The sequence is finite with largest term 1000000050000000400000000, corresponding to the quintuple {1, 1, 1, 100000001, 10000000400000000}. The growth of A382510 indicates that the number of terms might be in the order of 500000.
%C A384795 s occurs k times in the list if there exist k multisets {x_1,...,x_5} of natural numbers with s = Sum_{j=1..5} x_j = (1/100^4)*Product_{j=1..5} x_j.
%H A384795 Hugo Pfoertner, <a href="/A384795/b384795.txt">Table of n, a(n) for n = 1..10000</a>
%H A384795 Hugo Pfoertner, <a href="/A384795/a384795.txt">Solution quintuples sorted by sum, up to sum 5000</a>. (2025)
%e A384795 a(1) = 759 = 125 + 125 + 160 + 165 + 184; 1.25^2*1.6*1.65*1.84 = 7.59.
%e A384795 a(5) = a(6) = 770 = 125 + 125 + 140 + 160 + 220 = 110 + 125 + 160 + 175 + 200; 1.25^2*1.4*1.6*2.2 = 1.1*1.25*1.6*1.75*2.0 = 7.70.
%Y A384795 Cf. A380887, A381619, A381621, A382510.
%K A384795 nonn,fini
%O A384795 1,1
%A A384795 _Hugo Pfoertner_, Jun 15 2025