A382510 -id:A382510 - cp's OEIS frontend

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.

525, 540, 546, 549, 555, 561, 567, 570, 585, 588, 600, 612, 630, 642, 660, 660, 663, 675, 726, 735, 744, 750, 759, 765, 783, 792, 798, 810, 819, 825, 840, 840, 891, 897, 900, 930, 945, 957, 966, 966, 975, 981, 996, 1050, 1050, 1071, 1080, 1092, 1125, 1134, 1155, 1155, 1170

Offset: 1

Hugo Pfoertner and Markus Sigg, Mar 02 2025

The sequence has 622 terms. See linked files for all solutions.

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.

			a(1) = 525 because 1.50 + 1.75 + 2.00 = 1.50*1.75*2.00 = 5.25 is the solution with minimum sum;
a(15) = a(16) = 660 because there are 2 solutions:
  0.80 + 2.50 + 3.30 = 0.80*2.50*3.30 = 6.60 and
  1.10 + 1.50 + 4.00 = 1.10*1.50*4.00 = 6.60;
a(31) = a(32) = 840:
  0.60 + 2.80 + 5.00 = 0.60*2.80*5.00 = 8.40 and
  1.00 + 1.40 + 6.00 = 1.00*1.40*6.00 = 8.40;
a(622) = 100030002 is the largest term:
  0.01 + 100.01 + 1000200.00 = 0.01*100.01*1000200.00 = 1000300.02.

Hugo Pfoertner, Table of n, a(n) for n = 1..622
Hugo Pfoertner, Solution triples sorted by sum. (2025)
Hugo Pfoertner, Solution triples sorted by smallest price. (2025)
Eric Snyder and others, Finding solutions of sum a_i = product a_i = n, where the a_i are "price rationals", question in Mathematics StackExchange, Jun 29, 2022.

Cf. A380887, A381187, A381620, A381621, A382510.

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.

Original entry on oeis.org

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

Hugo Pfoertner, Mar 04 2025

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.

			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].

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)

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

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.

Original entry on oeis.org

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

Hugo Pfoertner, Jun 15 2025

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.

			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.

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

Cf. A380887, A381619, A381621, A382510.

cp's OEIS Frontend

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.

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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.

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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.

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