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A382933
Numbers k such that k, 2*m +- 3 and 3*m +- 2 are all semiprimes.
1
451, 707, 871, 1313, 1537, 1819, 1921, 1969, 2155, 2195, 2533, 2599, 2885, 2993, 3265, 3817, 3883, 3953, 3997, 4069, 4105, 4385, 4555, 4607, 5599, 5755, 5771, 6155, 6415, 6773, 7157, 7453, 7979, 8185, 8213, 8251, 8321, 8333, 8399, 8531, 9055, 9077, 9167, 9335, 9647, 9953, 9977, 10121, 10537
OFFSET
1,1
COMMENTS
All terms are odd.
The first term that is a square is a(241) = 49729 = 223^2.
LINKS
EXAMPLE
a(3) = 871 because 871 = 13 * 67,
2 * 871 - 3 = 1739 = 37 * 47,
2 * 871 + 3 = 1745 = 5 * 349,
3 * 871 - 2 = 2611 = 7 * 373, and
3 * 871 + 2 = 2615 = 5 * 523 are all semiprimes.
MAPLE
filter:= m -> andmap(t -> numtheory:-bigomega(t)=2, [m, 2*m-3, 2*m+3, 3*m-2, 3*m+2]):
select(filter, [seq(i, i=1..20000, 2)]);
MATHEMATICA
s = {}; Do [ If [ {2, 2, 2, 2, 2} == PrimeOmega [{m, 2*m - 3, 2*m
+ 3, 3*m - 2, 3*m + 2}], AppendTo [s, m]], {m, 5, 10^4, 2}]; s
CROSSREFS
Cf. A001358.
Sequence in context: A269763 A393862 A020268 * A345319 A066322 A128922
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Apr 15 2025
STATUS
approved