A360028 - OEIS

%I #20 Feb 15 2023 14:03:32

%S 1,1,1,16,1,11,1,11,30,30,79,17,44,28,12,30,150,144,252,304,20,300,

%T 132,12,252,234,18,112,32,456,52,520,60,28,120,180,162,2,52,324,42,

%U 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

%N Lexicographically earliest sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a semiprime.

%C The sequence cannot contain any semiprimes.

%C It appears that a(n) is always even for n > 11. - _Thomas Scheuerle_, Feb 15 2023

%H Thomas Scheuerle, <a href="/A360028/b360028.txt">Table of n, a(n) for n = 0..3999</a>

%e 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.

%o (MATLAB)

%o function a = A360028(max_n)

%o     a = 1; s = 1;

%o     while length(a) < max_n

%o         sn = [s+1 1];

%o         while(~isempty(find(arrayfun(@(x)(length(factor(x))),sn)==2, 1)))

%o             sn = sn+1;

%o         end

%o         s = sn; a = [a sn(end)];

%o     end

%o end % _Thomas Scheuerle_, Jan 22 2023

%Y Cf. A001358, A332941.

%K nonn

%O 0,4

%A _Ctibor O. Zizka_, Jan 22 2023