login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

The lesser of two consecutive numbers with at least 3 prime factors (counted with multiplicity).
1

%I #12 Sep 16 2022 13:39:25

%S 27,44,63,75,80,98,99,104,116,124,125,135,147,152,153,164,170,171,174,

%T 175,188,189,195,207,224,230,231,242,243,244,245,255,260,272,275,279,

%U 284,285,296,315,324,332,342,343,344,350,351,356,363,368,369,374,375,384,387,399

%N The lesser of two consecutive numbers with at least 3 prime factors (counted with multiplicity).

%C The first of two consecutive numbers in A033942.

%H Robert Israel, <a href="/A357077/b357077.txt">Table of n, a(n) for n = 1..10000</a>

%e 27 = 3^3 and 28 = 2^2 * 7. Thus, 27 and 28 both have at least three prime factors. Thus, 27 is in this sequence.

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

%p for n from 1 while count < 100 do

%p if numtheory:-bigomega(n) >= 3 then

%p if state = 1 then R:= R, n-1; count:= count+1

%p else state:= 1

%p fi

%p else state := 0

%p fi

%p od:

%p R; # _Robert Israel_, Sep 16 2022

%t Select[Range[1000], Total[Transpose[FactorInteger[#]][[2]]] >= 3 && Total[Transpose[FactorInteger[# + 1]][[2]]] >= 3 &]

%o (Python)

%o from sympy import factorint

%o def is033942(n): return sum(factorint(n).values()) > 2

%o def ok(n): return is033942(n) and is033942(n+1)

%o print([k for k in range(400) if ok(k)]) # _Michael S. Branicky_, Sep 10 2022

%Y Cf. A033942, A344843.

%K nonn

%O 1,1

%A _Tanya Khovanova_, Sep 10 2022