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A116017
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Numbers n such that n + sigma(n) is a repdigit.
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5
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1, 2, 3, 4, 5, 9, 34, 141, 198, 277, 297, 375, 499, 1420, 2651, 2777, 3554, 4999, 19050, 28660, 29128, 49999, 131061, 506311, 3844863, 3852517, 4761903, 4999999, 22222218, 37560831, 133878933, 506767303, 872011214, 1381799253, 1427435733
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| (1). If p=(10^(3n+2)-19)/27 is a prime greater than 3 then m=6p is in the sequence because m+sigma(m)=6*(10^(3n+2)-1)/9 (the proof is easy), so m+sigma(m) is a repdigit number. The smallest such terms is 22222218, the next such term is 6*(10^(3*430+2)-1)/9=222...218 which has 1292 digits. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
(2). If p=5*10^n-1 is prime then p is in the sequence because p+sigma(p)=10^(n+1)-1, so p+sigma(p) is a repdigit number. 499, 49999, 4999999,... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
(3). If p=(25*10^(n-1)-7)/9 is prime then p is in the sequence because p+sigma(p)=5*(10^n-1)/9, so p+sigma(p) is a repdigit number. 2, 277, 2777, 2777777777, ... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
(4). If p=(16*10^(n-1)-7)/9 is prime then m=2p is in the sequence because m+sigma(m)=8*(10^n-1) /9, so m+sigma(m) is a repdigit number. 34, 3554, 3555555554, ... are such terms. - Farideh Firoozbakht (m\ ymontain(AT)yahoo.com), Aug 17 2006, Dec 08 2007
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EXAMPLE
| 22222218+sigma(22222218)=66666666.
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MATHEMATICA
| Do[If[Length[Union[IntegerDigits[n + DivisorSigma[1, n]]]]==1, Print[n]], {n, 60000000}] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
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CROSSREFS
| Cf. A116018.
Sequence in context: A177064 A092233 A115895 * A067033 A067034 A039697
Adjacent sequences: A116014 A116015 A116016 * A116018 A116019 A116020
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KEYWORD
| nonn,base
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AUTHOR
| Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006
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EXTENSIONS
| One more term from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 19 2007
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