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A229271 Numbers k for which k + k' and k - k' are both prime, k' being the arithmetic derivative of k.

%I A229271 #12 Jul 28 2025 20:51:02
%S A229271 10,14,15,21,26,33,35,38,51,65,66,78,86,93,102,110,111,123,161,201,
%T A229271 203,206,209,215,221,230,258,278,282,321,371,374,395,398,402,413,438,
%U A229271 470,471,485,530,533,543,545,551,590,626,671,678,698,723,755,779,803,815
%N A229271 Numbers k for which k + k' and k - k' are both prime, k' being the arithmetic derivative of k.
%C A229271 Intersection of A165561 and A229269.
%H A229271 Paolo P. Lava, <a href="/A229271/b229271.txt">Table of n, a(n) for n = 1..1000</a>
%p A229271 with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
%p A229271 a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
%p A229271 if isprime(n+a) and isprime(n-a) then print(n); fi;
%p A229271 od; end: P(10^5);
%Y A229271 Cf. A003415, A165561, A165562, A229269, A229270, A229272.
%K A229271 nonn
%O A229271 1,1
%A A229271 _Paolo P. Lava_, Sep 18 2013