A376352 Squarefree semiprimes k such that k+1 is the product of three distinct primes and k+2 is the product of four distinct primes.

2413, 6193, 6697, 9469, 11065, 11233, 11893, 12153, 13333, 13393, 14005, 14089, 14233, 15293, 17113, 17533, 17833, 17869, 18613, 18653, 19693, 20053, 20557, 20613, 20733, 20893, 20993, 21145, 22033, 22285, 22405, 22693, 22753, 22969, 23329, 23413, 24033, 24493, 26101, 26453, 27113, 27553, 28117, 28453, 28741, 29053, 29353, 29713

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) == 1 (mod 4).

Example

2413 is a term because 2413 = 19*127 is the product of two distinct primes, 2414 = 2*17*71 is the product of three distinct primes and 2415 = 3*5*7*23 is the product of four distinct primes.
6193 is a term because 6193 = 11*563 is the product of two distinct primes, 6194 = 2*19*163 is the product of three distinct primes and 6195 = 3*5*7*59 is the product of four distinct primes.

Maple

q:= n-> andmap(j-> map(i-> i[2], ifactors(n+j-2)[2])=[1$j], [$2..4]):
select(q, [$1..30000])[];  # Alois P. Heinz, Sep 21 2024

Mathematica

Position[Partition[FactorInteger[#][[;; , 2]] & /@ Range[30000], 3, 1], {{1, 1}, {1, 1, 1}, {1, 1, 1, 1}}] // Flatten (* Amiram Eldar, Sep 21 2024 *)

Crossrefs

Cf. A006881, A007304, A046386, A328137.

Sequence in context: A323271 A283783 A260274 * A234126 A159346 A256835

Adjacent sequences: A376349 A376350 A376351 * A376353 A376354 A376355

Keyword

nonn

Author

Massimo Kofler, Sep 21 2024

Status

approved