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A067843 Least solution k>n of phi(k-n)+phi(k+n)=phi(2k).

%I A067843 #7 Jun 08 2018 20:31:43
%S A067843 5,10,7,10,11,12,35,14,13,22,55,22,19,70,19,22,85,26,77,26,27,110,55,
%T A067843 34,55,38,31,34,119,38,65,44,41,52,65,46,185,154,43,46,143,54,215,70,
%U A067843 57,110,161,58,187,68,67,76,203,62,175,62,61,76,95,74,67,130,71,88,95,82,115,74,73,130,215
%N A067843 Least solution k>n of phi(k-n)+phi(k+n)=phi(2k).
%C A067843 From _Robert Israel_, Jun 08 2018: (Start)
%C A067843 The first n for which a(n)-n is odd is 239.
%C A067843 If n+2 and n+4 are twin primes (i.e. n+2 is in A001359), then a(n) <= n+4.
%C A067843 Conjecture: a(n) >= n+4 for all n. (End)
%H A067843 Robert Israel, <a href="/A067843/b067843.txt">Table of n, a(n) for n = 1..10000</a>
%e A067843 k = 10 is the smallest solution of phi(k-2)+phi(k+2)=phi(2k). So a(2) = 10.
%p A067843 f:= proc(n) local k;
%p A067843      for k from n+1 do if numtheory:-phi(k-n)+numtheory:-phi(k+n)=numtheory:-phi(2*k) then return k fi od:
%p A067843 end proc:
%p A067843 map(f, [$1..100]); # _Robert Israel_, Jun 08 2018
%t A067843 f[k_] := Module[{i = k + 1}, While[EulerPhi[i - k] + EulerPhi[i + k] != EulerPhi[2 i], i++ ]; i]; Table[f[n], {n, 1, 40}]
%Y A067843 Cf. A000010, A067701.
%K A067843 nonn
%O A067843 1,1
%A A067843 _Joseph L. Pe_, Feb 11 2002
%E A067843 More terms from _Robert Israel_, Jun 08 2018