A147548 a(n) is the largest n-digit number m such that phi(10^n+1)=phi(m), gcd(10^n+1,m)=1 & 10 doesn't divide m and zero if there is no such m.

0, 0, 925, 9991, 95969, 995681, 9595969, 99820697, 894463345, 9992684743, 97451082703, 999896409437, 9935266565443, 99974409884813, 999999115863815, 9999446015088757, 99942773726308253, 999999997876532621, 9220779220779220841, 99999797970236297071

Offset

1,3

Comments

It is easily seen that if m is in the sequence then phi(m.m)=phi(m)^2 where dot means concatenation. So the sequence b(n)=a(n).a(n) is a subsequence of A147619 and it seems that the nenzero terms of this sequence is an infinite subsequence of the sequence 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

Table of n, a(n) for n=1..20.

Example

phi(894463345)=phi(10^9+1), gcd(10^9+1,894463345)=1, 10 doesn't divide 894463345 and 894463345 is the largesst 9-digit number number with these properties so a(9)=894463345. Note that phi(894463345.894463345)=phi(894463345)^2,

Mathematica

a[n_]:=(b=10^n+1; c=EulerPhi[b]; If[PrimeQ[b], 0, For[m=0, !(Mod[m, 10]>0&&GCD [10^n-m, b]==1&&c==EulerPhi[10^n-m]), m++ ]; 10^n-m]); Do[Print[a[n]], {n, 9}]

Crossrefs

Cf. A147547, A147549, A147619.

Sequence in context: A244169 A245791 A229641 * A116989 A152503 A099688

Adjacent sequences: A147545 A147546 A147547 * A147549 A147550 A147551

Keyword

base,nonn

Author

Farideh Firoozbakht, Nov 07 2008

Extensions

a(10)-a(14) from Max Alekseyev, Mar 12 2009

a(15)-a(20) from Hiroaki Yamanouchi, Aug 27 2014

Status

approved