A375239 Numbers k such that k, k+1, ..., k+5 all have 3 prime factors (counted with multiplicity).

2522, 4921, 18241, 25553, 27290, 40313, 90834, 95513, 98282, 98705, 117002, 120962, 136073, 136865, 148682, 153794, 181441, 181554, 185825, 211673, 211674, 212401, 215034, 216361, 231002, 231665, 234641, 236041, 236634, 266282, 281402, 285410, 298433, 298434, 330473, 331985, 346505, 381353

Offset: 1

Author

Zak Seidov and Robert Israel, Aug 06 2024

Keywords

• nonn

Comments

First differs from A045942 at position 20, where a(20) = 211673 but A045942(20) = 204323.

All terms == 1 or 2 (mod 8).

One of the numbers k, k+1, ..., k+5 is a Zumkeller number (A083207), since it is of the form 2*3*p, where p is prime > 3. - Ivan N. Ianakiev, Aug 08 2024

Examples

			a(3) = 18241 is a term because
  18241 = 17 * 29 * 37
  18242 =  2 * 7 * 1303
  18243 =  3^2 * 2027
  18244 =  2^2 * 4561
  18245 =  5 * 41 * 89
  18246 =  2 * 3 * 3041
are all products of 3 primes (counted with multiplicity).
		

Links

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

Crossrefs

Subsequence of A045942 and of A113789. Contains A259756.

Programs

Maple

R:= NULL: count:= 0: p:= 1:
while count < 100 do
  p:= nextprime(p);
  x:= 4*p;
  if andmap(t -> numtheory:-bigomega(t)=3, [x-2,x-1,x+1,x+2]) then
    if numtheory:-bigomega(x-3) = 3 then R:= R, x-3; count:= count+1;  fi;
    if numtheory:-bigomega(x+3) = 3 then R:= R, x-2; count:= count+1;  fi;
  fi;
od:
R;

Mathematica

s = {}; Do[If[{3, 3, 3, 3, 3, 3} == PrimeOmega[Range[k, k + 5]],
AppendTo[s, k]], {k, 1000000}]; s