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.

644, 651, 660, 663, 665, 672, 675, 675, 678, 680, 684, 684, 686, 689, 693, 693, 702, 705, 707, 707, 708, 711, 713, 714, 714, 720, 720, 720, 725, 726, 728, 728, 729, 735, 735, 735, 737, 747, 750, 752, 756, 756, 756, 756, 762, 765, 765, 765, 765, 767, 770, 770, 774, 774, 774, 777

Offset: 1

Author

Hugo Pfoertner, Mar 04 2025

Keywords

• nonn
• base
• fini

Comments

The sequence is finite with 22640 terms.

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.

Examples

			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;
a(7) = a(8) = 675 because there are 2 solutions:
  1.00 + 1.50 + 2.00 + 2.25 = 1.00*1.50*2.00*2.25 = 6.75 and
  1.20 + 1.25 + 1.80 + 2.50 = 1.20*1.25*1.80*2.50 = 6.75;
a(22) = 711 corresponds to the solution of the puzzle "The 7-Eleven" quoted from "The Guardian" in A380887.
a(22640) = 1000004000003 is the largest term, corresponding to the quadruple of prices [0.01, 0.01, 10000.01, 10000030000.00].
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000
• Hugo Pfoertner, Solution quadruples sorted by sum, up to sum 10^5. (2025)
• Hugo Pfoertner, Complete list of 22640 solution quadruples. (2025)

Crossrefs

Cf. A380887, A381187, A381619, A382508, A382510.