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%I #19 Dec 27 2015 17:19:38
%S 0,0,779,9991,90901,990001,9090901,94139561,681465373,9898047311,
%T 86925973487,979104060601,9080337988583,95255589092561,
%U 712493161316801,9926748805307137,90004044661864321,989999011990088281,9090909102763796801,97910150575731744097,713349371311332607153,9789743000892702875281,88299846937619669895601
%N Smallest n-digit number m such that phi(10^n+1)=phi(m), gcd(10^n+1,m)=1 and 10 does not divide m, or zero if there is no such m.
%C It is easily seen that if m is in the sequence, then phi(m.m)=phi(m)^2 where dot denotes concatenation. So the sequence b(n)=a(n).a(n) is a subsequence of A147619 and it seems that the nonzero terms of this sequence is an infinite subsequence of A147619. If 10^n+1 is prime (n must be of the form 2^k), then a(n)=0 because in this case there is no n-digit number m such that phi(10^n+1)=10^n=phi(m).
%H Max Alekseyev, <a href="/A147547/b147547.txt">Table of n, a(n) for n = 1..59</a>
%e phi(979104060601)=phi(10^12+1), gcd(10^12+1,979104060601)=1, 10 doesn't divide 979104060601 and 979104060601 is the smallest 12-digit number with these properties so a(12)=979104060601. Note that phi(979104060601.979104060601)=phi(979104060601)^2.
%t a[1]=a[2]=0;a[n_]:=(b=10^n+1;c=EulerPhi[b];For[m=c+1,!(Mod[m,10]>0&&GCD[m,b] ==1&&c==EulerPhi[m]),m++ ];m);Do[Print[a[n]],{n,12}]
%Y Cf. A147548, A147549, A147619.
%K base,nonn
%O 1,3
%A _Farideh Firoozbakht_, Nov 07 2008
%E a(13) and a(14) from _Max Alekseyev_, Mar 12 2009
%E a(15)-a(20) from _Hiroaki Yamanouchi_, Aug 27 2014
%E a(21)-a(59) from _Max Alekseyev_, Sep 07 2014, Dec 27 2015
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