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A116029
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Numbers n such that n + sigma(n) + phi(n) is a repdigit.
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1, 2, 3, 11, 12, 14, 16, 32, 37, 216, 325, 1851, 2962, 6836, 18125, 178569, 3652175, 7404814, 10599021, 196259690, 370355439
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All primes of the form 11...1 are in the sequence because if p=11...1 is a prime then sigma(p)+phi(p)+p=3p=33...3 is a repdigit number, so (10^A004023-1)/9 is a subsequence of this sequence. 37 is the only multi-digit prime term of the sequence which is not of the form 11...1 - the proof is easy. Next term is greater than 2.3*10^10. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
Also we have the following two assertions. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
(a). If p=(2*10^(3n+2)-11)/27 is prime then m=2p is in the sequence because sigma(m)+phi(m)+m=6p+2=4*(10^(3n+2)-1)/9 is a repdigit number. 2*(2*10^29-11)/27 (a 29-digit number)is the smallest such terms of the sequence and the next such term(if it exists) has more than 20000 digits. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
(b). If p=(4*10^(3n+1)-13)/27 is prime then m=2p is in the sequence because sigma(m)+phi(m)+m=8*(10^(3n+1)-1)/9 is a repdigit number. 2962 is the smallest such terms of the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
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EXAMPLE
| 3652175 + sigma(3652175) + phi(652175) = 11111111.
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CROSSREFS
| Cf. A116019.
Cf. A004023.
Sequence in context: A085305 A189818 A116032 * A060812 A172409 A062936
Adjacent sequences: A116026 A116027 A116028 * A116030 A116031 A116032
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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
| More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
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