A376503 - OEIS

%I #6 Sep 27 2024 23:14:10

%S 171869,5609369,7653119,11177069,11320709,11479319,12325619,13530119,

%T 15426419,15558119,17136619,17541869,17851919,18809369,18843119,

%U 19593869,19634369,19938119,20806619,21600419,22470953,23637839,23796869,23999369,24006119,24275819,25798739,25879001,25965869,26278169

%N Primes p such that p + 2, p + 4 and p + 6 are products  of 3, 5 and 7 primes respectively (counted with multiplicity)

%C Since 2 and 3 are not terms, the least possible prime factor of p + 6 is 5.  This is why, at least initially, it seems most terms end in 9.

%H Robert Israel, <a href="/A376503/b376503.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 7653119 is a term because 7653119 is prime,

%e 7653121 = 7 * 61 * 17923 has 3 prime factors,

%e 7653123 = 3^4 * 94483 has 5 prime factors, and

%e 7653125 = 5^5 * 31 * 79 has 7 prime factors, counted with multiplicity.

%p with(priqueue):

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

%p initialize(pq):

%p insert([-5^7,[5$7]],pq):

%p for iter from 1 while count < 100 do

%p   t:= extract(pq);

%p   v:= -t[1]; w:= t[2];

%p   if isprime(v-6) and numtheory:-bigomega(v-4) = 3 and numtheory:-bigomega(v-2) = 5 then

%p     R:= R,v-6; count:= count+1;

%p   fi;

%p   p:= nextprime(w[-1]);

%p   for i from 7 to 1 by -1 while w[i] = w[7] do

%p     insert([t[1]*(p/w[7])^(8-i),[op(w[1..i-1]),p$(8-i)]],pq);

%p   od;

%p od:

%p R;

%Y Cf. A001222, A255092.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Sep 25 2024