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A368078 Lexicographically earliest increasing sequence a(n) of products of 4 primes such that a(n) - a(n-1) and a(n) + a(n-1) are also products of 4 primes. The 4 primes are counted with multiplicity.

%I A368078 #21 Dec 30 2023 23:14:52
%S A368078 16,40,100,250,558,852,1062,1078,1628,1644,1794,2004,2020,2152,2292,
%T A368078 2418,2650,2706,2796,2812,3032,3116,3736,3796,3896,3956,3972,4026,
%U A368078 4450,4466,4794,5054,5094,5150,5525,5661,5697,5925,6201,6225,6325,6550,6566,6606,6756,6856,6956,7016,7076,8030,8214
%N A368078 Lexicographically earliest increasing sequence a(n) of products of 4 primes such that a(n) - a(n-1) and a(n) + a(n-1) are also products of 4 primes. The 4 primes are counted with multiplicity.
%C A368078 a(n) is the least number k > a(n-1) such that k, k - a(n-1), and k + a(n-1) are all in A014613.
%H A368078 Robert Israel, <a href="/A368078/b368078.txt">Table of n, a(n) for n = 1..10000</a>
%e A368078 a(3) = 100 because a(2) = 40 and 100 = 2^2 * 5^2, 100 - 40 = 60 = 2^2 * 3 * 5 and 100 + 40 = 140 = 2^2 * 4 * 7 are all in A014613.
%p A368078 isA014613:= proc(n) option remember; numtheory:-bigomega(n) = 4 end proc:
%p A368078 R:= 16: a:= 16: count:= 1:
%p A368078 while count < 100 do
%p A368078   for x from a+16 do
%p A368078     if isA014613(x-a) and isA014613(x) and isA014613(x+a) then break fi
%p A368078   od;
%p A368078   R:= R,x; a:= x; count:= count+1;
%p A368078 od:
%p A368078 R;
%t A368078 s = {m = 16}; Do[p = m + 16; While[{4, 4, 4} != PrimeOmega[{p, m +
%t A368078 p, p - m}], p++]; AppendTo[s, m = p], {50}]; s
%Y A368078 Cf. A014613, A361073.
%K A368078 nonn
%O A368078 1,1
%A A368078 _Zak Seidov_ and _Robert Israel_, Dec 11 2023