A376503 Primes p such that p + 2, p + 4 and p + 6 are products of 3, 5 and 7 primes respectively (counted with multiplicity)

171869, 5609369, 7653119, 11177069, 11320709, 11479319, 12325619, 13530119, 15426419, 15558119, 17136619, 17541869, 17851919, 18809369, 18843119, 19593869, 19634369, 19938119, 20806619, 21600419, 22470953, 23637839, 23796869, 23999369, 24006119, 24275819, 25798739, 25879001, 25965869, 26278169

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 7653119 is a term because 7653119 is prime,
7653121 = 7 * 61 * 17923 has 3 prime factors,
7653123 = 3^4 * 94483 has 5 prime factors, and
7653125 = 5^5 * 31 * 79 has 7 prime factors, counted with multiplicity.

Maple

with(priqueue):
R:= NULL: count:= 0:
initialize(pq):
insert([-5^7, [5$7]], pq):
for iter from 1 while count < 100 do
  t:= extract(pq);
  v:= -t[1]; w:= t[2];
  if isprime(v-6) and numtheory:-bigomega(v-4) = 3 and numtheory:-bigomega(v-2) = 5 then
    R:= R, v-6; count:= count+1;
  fi;
  p:= nextprime(w[-1]);
  for i from 7 to 1 by -1 while w[i] = w[7] do
    insert([t[1]*(p/w[7])^(8-i), [op(w[1..i-1]), p$(8-i)]], pq);
  od;
od:
R;

Crossrefs

Cf. A001222, A255092.

Sequence in context: A246227 A206115 A204730 * A049053 A242980 A221742

Adjacent sequences: A376500 A376501 A376502 * A376504 A376505 A376506

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 25 2024

Status

approved