A363391 - OEIS

%I #42 Jun 24 2023 01:24:15

%S 493,2413,3013,3427,3873,4333,4885,5029,5893,6697,7373,8373,10113,

%T 10533,13011,14005,14677,15122,16373,17173,17869,18613,19693,20053,

%U 20613,22417,23073,23077,23137,23573,24493,24613,24937,25141,26101,26193,26917,27637,27973,28357,29713,29941,31861,32393

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

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

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

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

%H Robert Israel, <a href="/A363391/b363391.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 R:= NULL: state:= 0: count:= 0:

%p for x from 1 while count < 50 do

%p   v:= numtheory:-bigomega(x);

%p   if v = 2 then state:= 2

%p   elif v = state+1 and state >= 2 then state:=state+1

%p   else state:= 0

%p   fi;

%p   if state = 5 then count:= count+1; R:= R,x-3;

%p   fi;

%p od:

%p R;

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

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Jun 23 2023