A369898 Numbers k such that k and k + 1 each have 9 prime divisors, counted with multiplicity.

203391, 698624, 1245375, 1942784, 2176064, 2282175, 2536191, 2858624, 2953664, 3282687, 3560192, 3655935, 3914000, 4068224, 4135616, 4205600, 4244967, 4586624, 4695488, 4744575, 4991679, 5055615, 5450624, 5475519, 5519744, 6141824, 6246800, 6410096, 6655040, 6660224, 6753375, 6816879, 6862400

Offset

1,1

Comments

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

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.

Links

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

Example

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.

Maple

with(priqueue):
R:= NULL:  count:= 0:
initialize(Q); r:= 0:
insert([-2^9, [2$9]], Q);
while count < 40 do
  T:= extract(Q);
  if -T[1] = r + 1 then
    R:= R, r; count:= count+1;
  fi;
  r:= -T[1];
  p:= T[2][-1];
  q:= nextprime(p);
  for i from 9 to 1 by -1 while T[2][i] = p do
    insert([-r*(q/p)^(10-i), [op(T[2][1..i-1]), q$(10-i)]], Q);
  od
od:
R;

Crossrefs

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

Sequence in context: A205891 A186532 A184455 * A210017 A176167 A248203

Adjacent sequences: A369895 A369896 A369897 * A369899 A369900 A369901

Keyword

nonn

Author

Robert Israel, Feb 04 2024

Status

approved