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A381621 Sorted list of sums of 4 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 A381621 #19 Jun 05 2025 13:00:31
%S A381621 644,651,660,663,665,672,675,675,678,680,684,684,686,689,693,693,702,
%T A381621 705,707,707,708,711,713,714,714,720,720,720,725,726,728,728,729,735,
%U A381621 735,735,737,747,750,752,756,756,756,756,762,765,765,765,765,767,770,770,774,774,774,777
%N A381621 Sorted list of sums of 4 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 A381621 The sequence is finite with 22640 terms.
%C A381621 A natural number s occurs k times in the list if there exist k multisets {a,b,c,d} of natural numbers with s = a + b + c + d and 100^3*s = a*b*c*d.
%H A381621 Hugo Pfoertner, <a href="/A381621/b381621.txt">Table of n, a(n) for n = 1..10000</a>
%H A381621 Hugo Pfoertner, <a href="/A381621/a381621.txt">Solution quadruples sorted by sum, up to sum 10^5</a>. (2025)
%H A381621 Hugo Pfoertner, <a href="/A381621/a381621_1.txt">Complete list of 22640 solution quadruples</a>. (2025)
%e A381621 a(1) = 644 = A380887(4) because 1.25 + 1.60 + 1.75 + 1.84 = 1.25*1.60*1.75*1.84 = 6.44 is the solution with minimum sum;
%e A381621 a(7) = a(8) = 675 because there are 2 solutions:
%e A381621   1.00 + 1.50 + 2.00 + 2.25 = 1.00*1.50*2.00*2.25 = 6.75 and
%e A381621   1.20 + 1.25 + 1.80 + 2.50 = 1.20*1.25*1.80*2.50 = 6.75;
%e A381621 a(22) = 711 corresponds to the solution of the puzzle "The 7-Eleven" quoted from "The Guardian" in A380887.
%e A381621 a(22640) = 1000004000003 is the largest term, corresponding to the quadruple of prices [0.01, 0.01, 10000.01, 10000030000.00].
%Y A381621 Cf. A380887, A381187, A381619, A382508, A382510.
%K A381621 nonn,base,fini
%O A381621 1,1
%A A381621 _Hugo Pfoertner_, Mar 04 2025