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