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A147547
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.
3
0, 0, 779, 9991, 90901, 990001, 9090901, 94139561, 681465373, 9898047311, 86925973487, 979104060601, 9080337988583, 95255589092561, 712493161316801, 9926748805307137, 90004044661864321, 989999011990088281, 9090909102763796801, 97910150575731744097, 713349371311332607153, 9789743000892702875281, 88299846937619669895601
OFFSET
1,3
COMMENTS
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).
LINKS
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Farideh Firoozbakht, Nov 07 2008
EXTENSIONS
a(13) and a(14) from Max Alekseyev, Mar 12 2009
a(15)-a(20) from Hiroaki Yamanouchi, Aug 27 2014
a(21)-a(59) from Max Alekseyev, Sep 07 2014, Dec 27 2015
STATUS
approved