A363391 Numbers k such that k, k+1, k+2, k+3 have 2, 3, 4, 5 prime factors respectively, counted with multiplicity.

493, 2413, 3013, 3427, 3873, 4333, 4885, 5029, 5893, 6697, 7373, 8373, 10113, 10533, 13011, 14005, 14677, 15122, 16373, 17173, 17869, 18613, 19693, 20053, 20613, 22417, 23073, 23077, 23137, 23573, 24493, 24613, 24937, 25141, 26101, 26193, 26917, 27637, 27973, 28357, 29713, 29941, 31861, 32393

Offset

1,1

Comments

Numbers k such that A001222(k+j) = 2+j for j = 0,1,2,3.

The first k in the sequence such that A001222(k+4) = 6 is a(232) = 153221.

The first k in the sequence such that A001222(k+4) = 6 and A001222(k+5) = 7 is a(4716) = 2940571.

Links

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

Example

a(3) = 3013 is a term because 3013 = 23 * 131 has 2 prime factors counted by multiplicity, 3014 = 2 * 11 * 137 has 3, 3015 = 3^2 * 5 * 67 has 4, and 3016 = 2^3 * 13 * 29 has 5.

Maple

R:= NULL: state:= 0: count:= 0:
for x from 1 while count < 50 do
  v:= numtheory:-bigomega(x);
  if v = 2 then state:= 2
  elif v = state+1 and state >= 2 then state:=state+1
  else state:= 0
  fi;
  if state = 5 then count:= count+1; R:= R, x-3;
  fi;
od:
R;

Crossrefs

Cf. A001222, A001358, A014612, A014613, A014614, A112998.

Sequence in context: A300058 A251540 A116207 * A264327 A045007 A062903

Adjacent sequences: A363388 A363389 A363390 * A363392 A363393 A363394

Keyword

nonn

Author

Zak Seidov and Robert Israel, Jun 23 2023

Status

approved