A369898 - OEIS

%I #7 Feb 05 2024 09:27:10

%S 203391,698624,1245375,1942784,2176064,2282175,2536191,2858624,

%T 2953664,3282687,3560192,3655935,3914000,4068224,4135616,4205600,

%U 4244967,4586624,4695488,4744575,4991679,5055615,5450624,5475519,5519744,6141824,6246800,6410096,6655040,6660224,6753375,6816879,6862400

%N Numbers k such that k and k + 1 each have 9 prime divisors, counted with multiplicity.

%C Numbers k such that k and k + 1 are in A046312.

%C If a and b are coprime terms of A046310, one of them even, then Dickson's conjecture implies there are infinitely many terms k where k/a and (k+1)/b are primes.

%H Robert Israel, <a href="/A369898/b369898.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 1245375 is a term because 1245375 = 3^5 * 5^3 * 41 and 1245376 = 2^6 * 11 * 29 * 61 each have 9 prime factors, counted with multiplicity.

%p with(priqueue):

%p R:= NULL:  count:= 0:

%p initialize(Q); r:= 0:

%p insert([-2^9, [2$9]], Q);

%p while count < 40 do

%p   T:= extract(Q);

%p   if -T[1] = r + 1 then

%p     R:= R, r; count:= count+1;

%p   fi;

%p   r:= -T[1];

%p   p:= T[2][-1];

%p   q:= nextprime(p);

%p   for i from 9 to 1 by -1 while T[2][i] = p do

%p     insert([-r*(q/p)^(10-i), [op(T[2][1..i-1]), q$(10-i)]], Q);

%p   od

%p od:

%p R;

%Y Cf. A001222, A046310, A046312, A115186, A369897.

%K nonn

%O 1,1

%A _Robert Israel_, Feb 04 2024