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

%I A363391 #42 Jun 24 2023 01:24:15
%S A363391 493,2413,3013,3427,3873,4333,4885,5029,5893,6697,7373,8373,10113,
%T A363391 10533,13011,14005,14677,15122,16373,17173,17869,18613,19693,20053,
%U A363391 20613,22417,23073,23077,23137,23573,24493,24613,24937,25141,26101,26193,26917,27637,27973,28357,29713,29941,31861,32393
%N A363391 Numbers k such that k, k+1, k+2, k+3 have 2, 3, 4, 5 prime factors respectively, counted with multiplicity.
%C A363391 Numbers k such that A001222(k+j) = 2+j for j = 0,1,2,3.
%C A363391 The first k in the sequence such that A001222(k+4) = 6 is a(232) = 153221.
%C A363391 The first k in the sequence such that A001222(k+4) = 6 and A001222(k+5) = 7 is a(4716) = 2940571.
%H A363391 Robert Israel, <a href="/A363391/b363391.txt">Table of n, a(n) for n = 1..10000</a>
%e A363391 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.
%p A363391 R:= NULL: state:= 0: count:= 0:
%p A363391 for x from 1 while count < 50 do
%p A363391   v:= numtheory:-bigomega(x);
%p A363391   if v = 2 then state:= 2
%p A363391   elif v = state+1 and state >= 2 then state:=state+1
%p A363391   else state:= 0
%p A363391   fi;
%p A363391   if state = 5 then count:= count+1; R:= R,x-3;
%p A363391   fi;
%p A363391 od:
%p A363391 R;
%Y A363391 Cf. A001222, A001358, A014612, A014613, A014614, A112998.
%K A363391 nonn
%O A363391 1,1
%A A363391 _Zak Seidov_ and _Robert Israel_, Jun 23 2023