login
Not-really primes: numbers n such that n - 1, n and n + 1 all have only 1 or 2 prime factors.
1

%I #16 Dec 16 2019 01:56:45

%S 3,4,5,6,10,14,22,34,38,58,86,94,122,142,158,178,202,214,218,302,382,

%T 394,446,502,542,634,698,718,842,878,922,1042,1138,1202,1262,1318,

%U 1346,1382,1402,1438,1622,1642,1762,1822,1838,1894,1942,1982,2018,2102

%N Not-really primes: numbers n such that n - 1, n and n + 1 all have only 1 or 2 prime factors.

%H Robert Israel, <a href="/A110300/b110300.txt">Table of n, a(n) for n = 1..6000</a>

%e 14 is in the sequence because 13, 14 and 15 have only 1, 2 and 2 prime factors respectively, viz. 13, 2 * 7 and 3 * 5.

%p S:= select(t -> numtheory:-bigomega(t) <= 2, {$2..3000}):

%p sort(convert(S intersect map(`+`,S,1) intersect map(`-`,S,1),list)); # _Robert Israel_, Dec 15 2019

%o (PARI) isok(n) = (bigomega(n-1)>0) && (bigomega(n-1)<=2) && (bigomega(n)<=2) && (bigomega(n+1)<=2) \\ _Michel Marcus_, Jul 23 2013

%Y Cf. A000040, A106639.

%K easy,nonn

%O 1,1

%A _Walter Nissen_, Aug 03 2005