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Search: id:A147548
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| A147548 |
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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. |
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3
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| 0, 0, 925, 9991, 95969, 995681, 9595969, 99820697, 894463345, 9992684743, 97451082703, 999896409437, 9935266565443, 99974409884813
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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).
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EXAMPLE
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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,
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A147547, A147549, A147619.
Sequence in context: A159701 A115696 A066741 this_sequence A116989 A152503 A099688
Adjacent sequences: A147545 A147546 A147547 this_sequence A147549 A147550 A147551
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KEYWORD
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more,base,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Nov 07 2008
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EXTENSIONS
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a(10)..a(14) from Max Alekseyev (maxale(AT)gmail.com), Mar 12 2009
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