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

1,1

Comments

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

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

Links

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

Example

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.

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));

Crossrefs

Cf. A001358, A092192.

Sequence in context: A251347 A346276 A234863 * A250695 A250680 A045307

Adjacent sequences: A362197 A362198 A362199 * A362201 A362202 A362203

Keyword

nonn

Author

Zak Seidov and Robert Israel, Apr 10 2023

Status

approved