

A088986


Numbers n such that each of n through n+4 are divisible by exactly two primes.


1



54, 91, 92, 115, 141, 142, 143, 144, 158, 205, 212, 213, 214, 215, 295, 301, 323, 324, 325, 391, 535, 685, 721, 799, 1135, 1345, 1465, 1535, 1711, 1941, 1981, 2101, 2215, 2302, 2303, 2304, 2425, 2641, 3865, 4411, 5461, 6505, 6625, 6925, 7165, 7231, 7261
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OFFSET

1,1


COMMENTS

Identical with A045933 from firstto 38th terms, but deviates later because A045933 includes start of chains with more than 2 primefactors.
Contrary to longer chains(6,7,8,..) of omega=2 this sequence seems to be either infinite or very long. See A088963A088985.
Primes counted without multiplicity. [Harvey P. Dale, Oct 20 2011]


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..750


EXAMPLE

n=9997771+j for j=0,1,2,3,4 has 2 distinct primefactors:
{7.1428253 # 4.2499443 # 3.3332591 # 2.4998887 # 25.399911}.


MATHEMATICA

Transpose[Select[Partition[Transpose[Select[Table[{n, PrimeNu[n]}, {n, 10000}], Last[#]==2&]][[1]], 5, 1], Last[#]First[#]==4&]][[1]] (* Harvey P. Dale, Oct 20 2011 *)


PROG

(Python)
from sympy import primefactors
def ok(n):
for i in range(5):
if len(primefactors(n + i))!=2: return 0
return 1
print [n for n in range(1, 8001) if ok(n)] # Indranil Ghosh, Jul 17 2017


CROSSREFS

Sequence in context: A290146 A071863 A045933 * A259717 A118150 A039779
Adjacent sequences: A088983 A088984 A088985 * A088987 A088988 A088989


KEYWORD

nonn


AUTHOR

Labos Elemer, Sep 30 2003


STATUS

approved



