A157489 Numbers n such that n-+5 are divisible by exactly 5 primes, counted with multiplicity.

275, 373, 445, 755, 985, 1165, 1245, 1475, 1535, 1643, 1645, 1705, 1715, 1745, 2219, 2305, 2317, 2389, 2445, 2455, 2543, 2579, 2845, 2855, 2893, 3229, 3299, 3325, 3371, 3565, 3613, 3659, 3695, 3757, 3829, 3875, 4255, 4285, 4295, 4345, 4355, 4477, 4745, 5003, 5065

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

• nonn

Comments

Let a, b and 10 be pairwise coprime, with A001222(a) = A001222(b) = 4. There exists c such that c == 5 (mod a) and c == -5 (mod b). Dickson's conjecture implies that (c+k*a*b-5)/a and (c+k*a*b+5)/b are prime for infinitely many k; for such k, c+k*a*b is in the sequence. - Robert Israel, Mar 22 2020

Links

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

Crossrefs

Cf. A001222, A124936, A014612, A157483, A157484, A157485, A157486

Programs

Maple

N:= 10^4: # for terms <= N
T5:= select(t -> numtheory:-bigomega(t)=5, {$1..N+5}):
S:= T5 intersect map(`+`,T5,10):
sort(convert(map(`-`,S,5),list)); # Robert Israel, Mar 22 2020

Mathematica

q=5;lst={};Do[If[Plus@@Last/@FactorInteger[n-q]==q&&Plus@@Last/@FactorInteger[n+q]==q,AppendTo[lst,n]],{n,8!}];lst
SequencePosition[PrimeOmega[Range[5100]],{5,,,_,,,_,,,_,5}][[All,1]]+5 (* Harvey P. Dale, Sep 23 2021 *)