[seqfan] Subsets with prime sums
zak seidov
zakseidov at yahoo.com
Sat Oct 24 17:31:32 CEST 2009
Dear seqfans,
Pending your
comments/editings/approvals/rejections/more_terms...
Thanks, Zak
%S A1
4,26,444,11998,382716
N A1
For each n, take n subsets of set 1..n^2.
Then select subsets with prime sums.
The sequence gives the
numbers of such subsets for n=2,3,4,5,6.
%e A1
n=2; a(2)=4 because there are four subsets of set {1,2,3,4} with prime sums:
{1,2}=>3
{1,4}=>5
{2,3}=>5
{3,4}=>7
n=3; a(3)=26 because there are 26 subsets of set {1,2,3,4,5,6,7,8,9}
{1,2,4},{1,2,8},{1,3,7},{1,3,9},{1,4,6},{1,4,8},{1,5,7},{1,7,9},{2,3,6},{2,3,8},{2,4,5},{2,4,7},{2,5,6},{2,6,9},{2,7,8},{2,8,9},{3,4,6},{3,5,9},{3,6,8},{3,7,9},{4,5,8},{4,6,7},{4,6,9},{4,7,8},{5,6,8},{6,8,9}
with corresponding prime sums:
{7,11,11,13,11,13,13,17,11,13,11,13,13,17,17,19,13,17,17,19,17,17,19,19,19,23}.
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