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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. 2
0, 0, 925, 9991, 95969, 995681, 9595969, 99820697, 894463345, 9992684743, 97451082703, 999896409437, 9935266565443, 99974409884813, 999999115863815, 9999446015088757, 99942773726308253, 999999997876532621, 9220779220779220841, 99999797970236297071 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)