A382933 Numbers k such that k, 2*m +- 3 and 3*m +- 2 are all semiprimes.

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

Author

Zak Seidov and Robert Israel, Apr 15 2025

Keywords

• nonn

Comments

All terms are odd.

The first term that is a square is a(241) = 49729 = 223^2.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358.

Programs

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