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%I #53 Oct 23 2022 01:21:23
%S 2,4,16,256,496,976,2626,3256,3706,5188,11716,13366,18316,22936,25546,
%T 46216,49216,49336,57646,65536,164176,184636,198316,215776,286996,
%U 307396,319276,388246,397486,415276,491536,568816,589408,686986,840256,914176,952576,983776
%N Solutions to A000010(x) + A000010(x-1) = A000010(2*x).
%C All terms are even. Does lim_{n->oo} log(a(n))/log(n) exist?
%C Are all terms except 2 congruent to 4 (mod 6)? - _Robert Israel_, Feb 27 2018 [a(3710) = 3044760173456 is the next term after 2 that is congruent to 2 (mod 6). - _Amiram Eldar_, Jul 17 2022]
%C Includes the Fermat numbers 2^(2^j)+1 for j = 0..5, but no other terms of A019434. - _Benoit Cloitre_, corrected by _Robert Israel_, Mar 02 2018
%C Even numbers k for which A000010(k) = A000010(k-1). - _Robert Israel_, Mar 02 2018
%H Amiram Eldar, <a href="/A299535/b299535.txt">Table of n, a(n) for n = 1..5416</a> (calculated using the b-file at A001274; terms 1..100 from Robert Israel)
%H Benoit Cloitre, <a href="/A299535/a299535.png">Plot of log(a(n))/log(n+1) for n=1 up to 62</a>
%p select(t -> numtheory:-phi(t)+ numtheory:-phi(t-1)=numtheory:-phi(2*t), [seq(i,i=2..10^6,2)]); # _Robert Israel_, Feb 27 2018
%o (PARI) for(n=2, 200000, if(eulerphi(n) + eulerphi(n-1) == eulerphi(2*n), print1(n, ",")))
%o (Magma) [n: n in [2..10^6] | EulerPhi(n)+EulerPhi(n-1) eq EulerPhi(2*n)]; // _Bruno Berselli_, Feb 27 2018
%Y Cf. A000010.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 27 2018
%E More terms from _Robert Israel_, Feb 27 2018
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