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Search: id:A147547
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| A147547 |
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a(n) is the smallest 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, 779, 9991, 90901, 990001, 9090901, 94139561, 681465373, 9898047311, 86925973487, 979104060601, 9080337988583, 95255589092561
(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(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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A147548, A147549, A147619.
Sequence in context: A043519 A043384 A008746 this_sequence A135198 A139400 A115467
Adjacent sequences: A147544 A147545 A147546 this_sequence A147548 A147549 A147550
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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(13) and a(14) from Max Alekseyev (maxale(AT)gmail.com), Mar 12 2009
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