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Search: id:A072393
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| A072393 |
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Numbers n such that n - reverse(n) = phi(n). |
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+0
3
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| 91, 874, 3411, 9093, 40112, 44252, 54081, 67284, 80224, 90933, 91503, 4961782, 5400081, 5726691, 8750834, 9076921, 9155055, 54000081, 62023914, 90766921, 93079231
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If m>1 and p=2*10^m+3 is prime then n=27*p is in the sequence because n-reversal(n)=27*(2*10^m+3)-reversal(27*(2*10^m+3))= (54*10^m+81)-(18*10^m+45)=36*10^m+36=18*(2*10^m+2)=phi(27)* phi(2*10^m+3)=phi(27*(2*10^m+3))=phi(n). Also if m>2 and p=(389*10^m+109)/3 is prime then 7*p is in the sequence (the proof is easy). Next term is greater than 2*10^8. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 27 2006
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EXAMPLE
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91 - 19 = 72 = phi(91), so 91 is a term of the sequence.
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MATHEMATICA
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Select[Range[10^5], # - FromDigits[Reverse[IntegerDigits[n]]] == EulerPhi[ # ] &]
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CROSSREFS
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Cf. A114926, A114927.
Sequence in context: A047696 A043459 A038488 this_sequence A085952 A129255 A093291
Adjacent sequences: A072390 A072391 A072392 this_sequence A072394 A072395 A072396
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KEYWORD
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base,nonn
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AUTHOR
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Joseph L. Pe (JosephL.Pe(AT)hotmail.com), Jul 21 2002
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EXTENSIONS
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More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 27 2006
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