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A157489 Numbers n such that n-+5 are divisible by exactly 5 primes, counted with multiplicity. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 17:36 EDT 2022. Contains 356122 sequences. (Running on oeis4.)