A361365 a(n) is the minimum possible sum of 2*n distinct positive numbers in a set, arranged in two subsets of size n each, such that the sum of any one element in each of the two subsets is a prime number.
3, 10, 29, 90, 207, 384, 689, 1226, 2523, 4446, 7919
Offset: 1
Examples
a(1) = 3, the minimum possible sum of two distinct numbers in the set. These add up to 3, which is a prime.
1 2
a(2) = 10, the least possible sum of four distinct numbers in the set. Any number from the first column added to any number in the second, gives a prime number. There are 2^2 = 4 possibilities, e.g., 1 + 4 = 5, or 3 + 4 = 7, and so on.
1 2
3 4
a(3) = 29, the minimum possible sum of six distinct numbers in the set. Any number in the first column added to any number in the second, results in a prime number. There are 3^2 = 9 possibilities, e.g., 1 + 10 = 11, or 9 + 4 = 13, and so on.
1 2
3 4
9 10
a(4) = 90 is attained in two different ways,
sets {1,5,11,17} {2,6,12,36}
or sets {1,5,11,35} {2,6,12,18}
Links
- Kevin Ryde, C Code
Programs
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C
/* See links */
Extensions
a(4)-a(11) from Kevin Ryde, Mar 23 2023
Comments