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A361073 Lexicographically least increasing sequence of triprimes (A014612) a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also triprimes.

%I A361073 #38 Apr 10 2023 01:41:00
%S A361073 8,20,50,125,279,426,531,539,814,822,897,1002,1010,1076,1146,1209,
%T A361073 1325,1353,1398,1406,1516,1558,1868,1898,1948,1978,1986,2013,2225,
%U A361073 2233,2397,2527,2547,2575,2763,2783,2810,2908,2938,2946,3009,3054,3081,3414,3422,3452,3522,3567,3714,3759,3786,3813
%N A361073 Lexicographically least increasing sequence of triprimes (A014612) a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also triprimes.
%H A361073 Robert Israel, <a href="/A361073/b361073.txt">Table of n, a(n) for n = 1..10000</a>
%e A361073 a(3) = 50 because 50 = 2^2*5, 50 - a(2) = 30 = 2*3*5 and 50 + a(2) = 70 = 2*5*7 are all products of 3 (not necessarily distinct) primes, and 50 is the least number that works.
%p A361073 A[1]:= 8:
%p A361073 for i from 2 to 100 do
%p A361073   for x from A[i-1]+8 do
%p A361073     if numtheory:-bigomega(x) = 3 and numtheory:-bigomega(x-A[i-1]) = 3 and numtheory:-bigomega(x+A[i-1]) = 3 then
%p A361073        A[i]:= x; break
%p A361073     fi
%p A361073 od od:
%p A361073 seq(A[i],i=1..100);
%t A361073 s = {m = 8}; Do[p = m + 8; While[{3, 3, 3} != PrimeOmega[{p, m + p,
%t A361073 p - m}], p++];  AppendTo[s, m = p], {50}]; s
%Y A361073 Cf. A014612, A361611, A361215.
%K A361073 nonn
%O A361073 1,1
%A A361073 _Zak Seidov_ and _Robert Israel_, Apr 09 2023