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A365145 Lexicographically least increasing sequence of triprimes (A014612) whose first differences are triprimes.

%I A365145 #6 Aug 24 2023 10:17:18
%S A365145 8,20,28,70,78,98,110,130,138,165,195,207,273,285,363,426,434,442,470,
%T A365145 498,506,518,530,548,556,574,582,590,598,606,618,638,646,654,682,710,
%U A365145 722,730,742,754,762,782,790,834,854,874,892,942,962,970,978,986,994,1002,1010,1022,1030,1038,1058
%N A365145 Lexicographically least increasing sequence of triprimes (A014612) whose first differences are triprimes.
%C A365145 a(n) - a(n-1) >= 8.  If a(n-1) = 4*p where p is in A001359 then a(n) - a(n-1) = 8.
%H A365145 Robert Israel, <a href="/A365145/b365145.txt">Table of n, a(n) for n = 1..10000</a>
%e A365145 a(2) = 20, a(3) = 28 = 2^2 * 7 is a triprime and 28 - 20 = 8 = 2^3 is a triprime, and this is the least number > 20 that works, so a(4) = 28.
%p A365145 R:= 8: m:= 8: count:= 1:
%p A365145 for t from 9 while count < 100 do
%p A365145   if numtheory:-bigomega(t) = 3 and numtheory:-bigomega(t-m) = 3 then
%p A365145     R:= R,t; m:= t; count:= count+1
%p A365145   fi
%p A365145 od:
%p A365145 R;
%t A365145 Do[n = m + 8; While[{3, 3} != PrimeOmega[{n, n - m}],
%t A365145 n++]; AppendTo[s, m = n], {100}]; s
%Y A365145 Cf. A001359, A014612, A175588.
%K A365145 nonn
%O A365145 1,1
%A A365145 _Zak Seidov_ and _Robert Israel_, Aug 23 2023