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A360028
Lexicographically earliest sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a semiprime.
1
1, 1, 1, 16, 1, 11, 1, 11, 30, 30, 79, 17, 44, 28, 12, 30, 150, 144, 252, 304, 20, 300, 132, 12, 252, 234, 18, 112, 32, 456, 52, 520, 60, 28, 120, 180, 162, 2, 52, 324, 42, 130, 20, 60, 100, 92, 132, 126, 186, 184, 104, 12, 104, 320, 8, 12, 20, 320, 104, 16, 32, 208, 404, 240, 300, 60, 408
OFFSET
0,4
COMMENTS
The sequence cannot contain any semiprimes.
It appears that a(n) is always even for n > 11. - Thomas Scheuerle, Feb 15 2023
LINKS
EXAMPLE
a(0) = 1 by the definition of the sequence. For the next number we try 1; {1, 1 + 1} are not semiprimes, thus a(1) = 1. For the next number we try 1; {1, 1 + 1, 1 + 1 + 1} are not semiprimes, thus a(2) = 1.
PROG
(MATLAB)
function a = A360028(max_n)
a = 1; s = 1;
while length(a) < max_n
sn = [s+1 1];
while(~isempty(find(arrayfun(@(x)(length(factor(x))), sn)==2, 1)))
sn = sn+1;
end
s = sn; a = [a sn(end)];
end
end % Thomas Scheuerle, Jan 22 2023
CROSSREFS
Sequence in context: A040268 A321673 A040269 * A141682 A040270 A303327
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Jan 22 2023
STATUS
approved