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A358438 a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiprime number > a(n) such that the sum of any three consecutive terms is a semiprime.

%I A358438 #25 Dec 17 2022 05:56:19
%S A358438 4,6,15,25,34,35,46,62,69,74,94,106,119,121,122,134,142,146,158,169,
%T A358438 178,206,213,214,235,249,253,265,267,299,303,319,321,334,382,395,422,
%U A358438 445,446,454,466,469,482,514,517,538,586,589,591,623,629
%N A358438 a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiprime number > a(n) such that the sum of any three consecutive terms is a semiprime.
%C A358438 Do even numbers thin out as you look at larger and larger numbers of terms? - _Charles R Greathouse IV_, Nov 18 2022
%H A358438 Robert Israel, <a href="/A358438/b358438.txt">Table of n, a(n) for n = 1..10000</a>
%e A358438 4 + 6 + 15 = 25 = 5*5, 6 + 15 + 25 = 46 = 2*23.
%p A358438 R:= 4,6:
%p A358438 for i from 3 to 100 do
%p A358438   s:= R[i-2]+R[i-1];
%p A358438   for t from R[i-1]+1 do
%p A358438     if numtheory:-bigomega(t) = 2 and numtheory:-bigomega(s+t)=2 then
%p A358438       R:= R, t; break
%p A358438     fi
%p A358438 od od:
%p A358438 R; # _Robert Israel_, Nov 18 2022
%t A358438 s = {4, 6}; p = 4; q = 6; r = q + 1; Do[While[2 != PrimeOmega[r] || 2 != PrimeOmega[p + q + r], r++]; AppendTo[s, r]; p = q; q = r; r++, {100}]; s
%Y A358438 Cf. A062391 (analog for primes), A001358 (semiprimes).
%K A358438 nonn
%O A358438 1,1
%A A358438 _Zak Seidov_, Nov 17 2022