

A328815


The smallest k such that one can form two sets of size n with distinct numbers from 1 to k with the property that the sum of any pair of numbers from different sets is a prime.


0



2, 4, 10, 31, 45, 85, 151, 253, 420, 775, 1303, 2521, 4641
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(10) <= 775, because we can form these two sets:
{1, 61, 115, 151, 271, 295, 325, 361, 661, 775}
{12, 22, 162, 196, 348, 448, 462, 502, 658, 768}.
a(11) <= 1303, because we can form these two sets:
{4, 16, 58, 136, 178, 256, 268, 508, 586, 796, 1048}
{1, 13, 15, 133, 175, 253, 483, 505, 925, 1035, 1303}.


LINKS

Table of n, a(n) for n=1..13.
Dmitry Kamenetsky, Two equalsized lists that produce prime sums, Puzzling StackExchange, 2019.


EXAMPLE

For n=3 one can use the sets {1, 3, 9} and {2, 4, 10}. The sum of every pair of numbers from different sets is prime: 1+2 = 3, 1+4 = 5, 1+10 = 11, 3+2 = 5, 3+4 = 7, 3+10 = 13, 9+2 = 11, 9+4 = 13, 9+10 = 19. The largest number in these sets is 10, hence a(3) = 10.
From Bert Dobbelaere, Nov 17 2019: (Start)
a(12) = 2521. One of the two solutions with all elements <= 2521 is the pair of sets
{1, 19, 49, 79, 175, 415, 595, 1405, 1531, 2311, 2359, 2521}
{88, 162, 192, 382, 568, 598, 708, 1012, 1152, 2062, 2202, 2292} (End).
From Bert Dobbelaere, Nov 20 2019: (Start)
a(13) = 4641. Unique solution is the pair of sets
{1, 21, 135, 561, 735, 1045, 1801, 1825, 2445, 3355, 3661, 3705, 4641}
{172, 262, 556, 592, 862, 886, 1018, 1732, 1978, 1996, 2656, 3592, 4462} (End).


CROSSREFS

Sequence in context: A280432 A001647 A007177 * A242347 A138415 A005268
Adjacent sequences: A328812 A328813 A328814 * A328816 A328817 A328818


KEYWORD

nonn,more,hard


AUTHOR

Dmitry Kamenetsky, Oct 28 2019


EXTENSIONS

a(10)a(12) from Bert Dobbelaere, Nov 17 2019
a(13) from Bert Dobbelaere, Nov 20 2019


STATUS

approved



