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Numbers m such that m-3 and m+3 have 3 prime factors.
3

%I #16 May 07 2023 12:09:23

%S 15,47,73,95,102,113,127,150,151,167,168,185,233,239,241,258,276,282,

%T 287,289,313,319,335,360,366,407,409,415,426,431,432,433,439,480,521,

%U 527,552,558,593,599,601,606,607,612,642,648,649,654,655,660,708,713

%N Numbers m such that m-3 and m+3 have 3 prime factors.

%C A001222(a(n)-3) = A001222(a(n)+3) = 3.

%C Prime factors counted with multiplicity. - _Harvey P. Dale_, May 07 2023

%H Harvey P. Dale, <a href="/A105572/b105572.txt">Table of n, a(n) for n = 1..1000</a>

%e From _Jon E. Schoenfield_, Jan 19 2015: (Start)

%e 73 - 3 = 70 = 2 * 5 * 7 and 73 + 3 = 76 = 2 * 2 * 19 so 73 is in the sequence.

%e 81 - 3 = 78 = 2 * 3 * 13 but 81 + 3 = 84 = 2 * 2 * 3 * 7 so 81 is not in the sequence. (End)

%t q=3;lst={};Do[If[Plus@@Last/@FactorInteger[n-q]==q&&Plus@@Last/@FactorInteger[n+q]==q,AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2009 *)

%t Flatten[Position[Partition[PrimeOmega[Range[800]],7,1],_?(#[[1]]==#[[7]]==3&),1,Heads-> False]]+3 (* _Harvey P. Dale_, May 07 2023 *)

%Y Cf. A014574, A105571, A105573.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 14 2005