A362200 Semiprimes k such that k+1, k+2, 2*k+1 and 2*k+3 are also semiprimes.

11733, 15117, 17245, 28113, 32365, 34413, 48745, 78481, 93453, 101665, 102957, 105333, 108753, 134097, 143101, 157713, 163801, 170853, 190621, 208293, 212545, 233097, 273417, 274893, 294301, 300385, 323281, 346497, 354565, 363777, 390205, 405357, 470341, 500217, 501477, 542193, 555153, 561205

Offset: 1

Author

Zak Seidov and Robert Israel, Apr 10 2023

Keywords

• nonn

Comments

Numbers k such that 2*k+1 and 2*k+3 are both in A092192.

All terms == 1 or 33 (mod 36).

Examples

			a(3) = 17245 is a term because 17245 = 5 * 3449, 17246 = 2 * 8623, 17247 = 3 * 5749, 2 * 17245 + 1 = 34491 = 3 * 11497 and 2 * 17245 + 3 = 34493 = 17 * 2029 are all semiprimes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A092192.

Programs

Maple

SP:= select(t -> numtheory:-bigomega(t)=2, {$1..2*10^6}):
A:= SP intersect map(`-`,SP,1) intersect map(`-`,SP,2):
SPO:= select(type,SP,odd):
A:= A intersect map(t -> (t-1)/2, SPO) intersect map(t -> (t-3)/2, SPO):
sort(convert(A,list));