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A072393
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Numbers n such that n - reverse(n) = phi(n).
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2
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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, 430770922, 540000081, 636355044, 808618664, 907666921, 928709013, 4050394312, 4262971312
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| 91 - 19 = 72 = phi(91), so 91 is a term of the sequence.
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MATHEMATICA
| Select[Range[10^5], # - FromDigits[Reverse[IntegerDigits[n]]] == EulerPhi[ # ] &]
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CROSSREFS
| Cf. A114926, A114927.
Sequence in context: A047696 A043459 A038488 * A085952 A129255 A093291
Adjacent sequences: A072390 A072391 A072392 * A072394 A072395 A072396
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KEYWORD
| base,nonn
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AUTHOR
| Joseph L. Pe (JosephL.Pe(AT)hotmail.com), Jul 21 2002
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EXTENSIONS
| More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 27 2006
a(22)-a(29) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 04 2011
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