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Lexicographically least increasing sequence of triprimes whose first differences are semiprimes.
1

%I #8 Aug 12 2023 00:43:49

%S 8,12,18,27,42,52,66,70,76,98,102,116,125,147,153,174,188,222,231,245,

%T 255,261,275,279,285,310,316,322,332,338,363,369,402,406,410,425,429,

%U 435,470,474,483,498,507,556,578,582,596,602,606,610,645,651,657,663,678,682,692,725,747,762,772,782

%N Lexicographically least increasing sequence of triprimes whose first differences are semiprimes.

%C For n >= 2, a(n) is the least member k of A014612 such that k - a(n-1) is in A001358.

%H Robert Israel, <a href="/A364776/b364776.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 27 because a(3) = 18, 27 = 3^3 is a triprime, and 27 - 18 = 9 = 3^2 is a semiprime.

%p R:= 8: count:= 1: x:= 8:

%p for i from 9 while count < 100 do

%p if numtheory:-bigomega(i) = 3 and numtheory:-bigomega(i-x) = 2 then

%p R:= R,i; count:= count+1; x:= i;

%p fi

%p od:

%p R;

%t s = {8, 12, 18, m=27}; Do[n = m + 4; While[3 != PrimeOmega[n] || 2

%t != PrimeOmega[n - m], n++]; AppendTo[s, m = n], {100}]; s

%Y Cf. A001358, A014612.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Aug 06 2023