A157483 Numbers k such that k-1 and k+1 are divisible by exactly 3 primes, counted with multiplicity.

19, 29, 43, 51, 67, 69, 77, 115, 171, 173, 187, 189, 237, 243, 245, 267, 274, 283, 285, 291, 317, 344, 355, 386, 403, 405, 411, 424, 427, 429, 435, 437, 476, 507, 597, 603, 604, 605, 638, 653, 664, 669, 723, 763, 776, 787, 789, 846, 891, 893, 907, 926, 963

Offset

1,1

Comments

Omega(a(n) - 1) = Omega(a(n) + 1) = 3, where Omega(n)=A001222(n). In general twin k-almost prime pairs are defined by Omega(a(n) - 1) = Omega(a(n) + 1) = k. Twin 1-almost primes are twin prime pairs (A014574). - Redjan Shabani, Jul 20 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

19 is a term: 19-1 = 18 = 2*3*3 and 19+1 = 20 = 2*2*5.

Maple

with(numtheory); a := proc (n) if bigomega(n-1) = 3 and bigomega(n+1) = 3 then n else end if end proc: seq(a(n), n = 2 .. 1100); # Emeric Deutsch, Mar 03 2009

Mathematica

q=3; lst={}; Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q, AppendTo[lst, n]], {n, 7!}]; lst
Mean/@SequencePosition[PrimeOmega[Range[1000]], {3, _, 3}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 21 2020 *)

Prog

(PARI) is(n)=bigomega(n-1)==3 && bigomega(n+1)==3 \\ Charles R Greathouse IV, Feb 05 2017

Crossrefs

Cf. A124936, A014612, A156028.

Sequence in context: A274849 A276049 A108183 * A173966 A096218 A100590

Adjacent sequences: A157480 A157481 A157482 * A157484 A157485 A157486

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Extensions

More terms from Emeric Deutsch, Mar 03 2009

Status

approved