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

1,1

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

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 *)

Crossrefs

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

Sequence in context: A070272 A066127 A062377 * A144715 A321487 A250736

Adjacent sequences: A157486 A157487 A157488 * A157490 A157491 A157492

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Status

approved