cp's OEIS Frontend

A360028 Lexicographically earliest sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a semiprime.

%I A360028 #20 Feb 15 2023 14:03:32
%S A360028 1,1,1,16,1,11,1,11,30,30,79,17,44,28,12,30,150,144,252,304,20,300,
%T A360028 132,12,252,234,18,112,32,456,52,520,60,28,120,180,162,2,52,324,42,
%U A360028 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 A360028 Lexicographically earliest sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a semiprime.
%C A360028 The sequence cannot contain any semiprimes.
%C A360028 It appears that a(n) is always even for n > 11. - _Thomas Scheuerle_, Feb 15 2023
%H A360028 Thomas Scheuerle, <a href="/A360028/b360028.txt">Table of n, a(n) for n = 0..3999</a>
%e A360028 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 A360028 (MATLAB)
%o A360028 function a = A360028(max_n)
%o A360028     a = 1; s = 1;
%o A360028     while length(a) < max_n
%o A360028         sn = [s+1 1];
%o A360028         while(~isempty(find(arrayfun(@(x)(length(factor(x))),sn)==2, 1)))
%o A360028             sn = sn+1;
%o A360028         end
%o A360028         s = sn; a = [a sn(end)];
%o A360028     end
%o A360028 end % _Thomas Scheuerle_, Jan 22 2023
%Y A360028 Cf. A001358, A332941.
%K A360028 nonn
%O A360028 0,4
%A A360028 _Ctibor O. Zizka_, Jan 22 2023