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A173085 Numbers n such that n, n^2 - 5, and n^2 + 5 are semiprime. 3
26, 62, 86, 118, 134, 566, 706, 982, 1198, 1322, 1346, 1678, 1706, 1822, 2386, 2402, 2498, 2654, 2966, 3086, 3142, 3158, 3326, 3662, 4222, 4874, 5158, 5354, 5774, 6602, 6638, 6746, 6998, 7142, 7586, 7646, 7834, 8006, 8482, 8486, 8846, 9134, 9406, 10558 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
26^2-5=671 -> 11*61, 26^2+5=681 -> 3*227,..
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) >> n log n. - Charles R Greathouse IV, Sep 14 2015
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-5; b=n^2+5; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 9!}]; lst
Select[Range[12000], PrimeOmega[#]==PrimeOmega[#^2-5] == PrimeOmega[ #^2+5] == 2&] (* Harvey P. Dale, Aug 29 2021 *)
PROG
(PARI) issemi(n)=bigomega(n)==2
is(n)=if(n%2, isprime((n^2-5)\2) && isprime((n^2+5)\2) && issemi(n), isprime(n/2) && issemi(n^2-5) && issemi(n^2+5)) \\ Charles R Greathouse IV, Sep 14 2015
CROSSREFS
Sequence in context: A291105 A267294 A162316 * A044128 A044509 A039413
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Charles R Greathouse IV, Apr 06 2010
STATUS
approved

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Last modified June 16 18:41 EDT 2024. Contains 373432 sequences. (Running on oeis4.)