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.

2, 4, 10, 31, 45, 85, 151, 253, 420, 775, 1303, 2521, 4641

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 equal-sized 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