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.

759, 760, 762, 765, 770, 770, 774, 777, 779, 780, 780, 780, 783, 783, 784, 785, 786, 791, 791, 792, 792, 792, 795, 798, 798, 798, 798, 798, 799, 799, 800, 804, 804, 805, 805, 805, 806, 808, 810, 810, 810, 810, 810, 810, 810, 810, 812, 812, 813, 816, 816, 816, 817, 817, 817

Offset: 1

Author

Hugo Pfoertner, Jun 15 2025

Keywords

• nonn
• fini

Comments

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.

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.

Examples

			a(1) = 759 = 125 + 125 + 160 + 165 + 184; 1.25^2*1.6*1.65*1.84 = 7.59.
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.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000
• Hugo Pfoertner, Solution quintuples sorted by sum, up to sum 5000. (2025)

Crossrefs

Cf. A380887, A381619, A381621, A382510.