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A375239
Numbers k such that k, k+1, ..., k+5 all have 3 prime factors (counted with multiplicity).
1
2522, 4921, 18241, 25553, 27290, 40313, 90834, 95513, 98282, 98705, 117002, 120962, 136073, 136865, 148682, 153794, 181441, 181554, 185825, 211673, 211674, 212401, 215034, 216361, 231002, 231665, 234641, 236041, 236634, 266282, 281402, 285410, 298433, 298434, 330473, 331985, 346505, 381353
OFFSET
1,1
COMMENTS
First differs from A045942 at position 20, where a(20) = 211673 but A045942(20) = 204323.
All terms == 1 or 2 (mod 8).
One of the numbers k, k+1, ..., k+5 is a Zumkeller number (A083207), since it is of the form 2*3*p, where p is prime > 3. - Ivan N. Ianakiev, Aug 08 2024
LINKS
EXAMPLE
a(3) = 18241 is a term because
18241 = 17 * 29 * 37
18242 = 2 * 7 * 1303
18243 = 3^2 * 2027
18244 = 2^2 * 4561
18245 = 5 * 41 * 89
18246 = 2 * 3 * 3041
are all products of 3 primes (counted with multiplicity).
MAPLE
R:= NULL: count:= 0: p:= 1:
while count < 100 do
p:= nextprime(p);
x:= 4*p;
if andmap(t -> numtheory:-bigomega(t)=3, [x-2, x-1, x+1, x+2]) then
if numtheory:-bigomega(x-3) = 3 then R:= R, x-3; count:= count+1; fi;
if numtheory:-bigomega(x+3) = 3 then R:= R, x-2; count:= count+1; fi;
fi;
od:
R;
MATHEMATICA
s = {}; Do[If[{3, 3, 3, 3, 3, 3} == PrimeOmega[Range[k, k + 5]],
AppendTo[s, k]], {k, 1000000}]; s
CROSSREFS
Subsequence of A045942 and of A113789. Contains A259756.
Sequence in context: A217588 A264339 A045942 * A308735 A096026 A278003
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Aug 06 2024
STATUS
approved