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A229272 Numbers n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n.

%I A229272 #18 Oct 16 2024 14:52:36
%S A229272 210,330,390,690,798,966,1110,1230,2190,2310,2730,3270,4110,4530,4890,
%T A229272 5430,6090,6270,6810,6990,7230,7890,8310,8490,9030,9210,9282,10470,
%U A229272 10590,10770,12090,12210,12270,12570,12810,12930,13110,13830,14070,17070,17094,17310
%N A229272 Numbers n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n.
%C A229272 Intersection of A165561 and A229270.
%H A229272 Paolo P. Lava, <a href="/A229272/b229272.txt">Table of n, a(n) for n = 1..300</a>
%p A229272 with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
%p A229272 a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
%p A229272 if isprime(a+n) and isprime(a-n) then print(n); fi;
%p A229272 od; end: P(10^5);
%o A229272 (Python)
%o A229272 from sympy import isprime, factorint
%o A229272 A229272 = []
%o A229272 for n in range(1, 10**5):
%o A229272     np = sum([int(n*e/p) for p, e in factorint(n).items()]) if n > 1 else 0
%o A229272     if isprime(np+n) and isprime(np-n):
%o A229272         A229272.append(n)
%o A229272 # _Chai Wah Wu_, Aug 21 2014
%Y A229272 Cf. A003415, A165561, A165562, A229269-A229271.
%K A229272 nonn
%O A229272 1,1
%A A229272 _Paolo P. Lava_, Sep 18 2013