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 A116029 Numbers n such that n + sigma(n) + phi(n) is a repdigit. 0
 1, 2, 3, 11, 12, 14, 16, 32, 37, 216, 325, 1851, 2962, 6836, 18125, 178569, 3652175, 7404814, 10599021, 196259690, 370355439, 2962962962, 7355242534, 7404880354, 31328532351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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, Aug 24 2006 Also we have the following two assertions. - Farideh Firoozbakht, 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, 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, Aug 24 2006 a(26) > 10^11. - Donovan Johnson, Feb 19 2013 LINKS Table of n, a(n) for n=1..25. EXAMPLE 3652175 + sigma(3652175) + phi(3652175) = 11111111. CROSSREFS Cf. A116019, A004023. Sequence in context: A085305 A189818 A116032 * A060812 A212129 A172409 Adjacent sequences: A116026 A116027 A116028 * A116030 A116031 A116032 KEYWORD nonn,base AUTHOR Giovanni Resta, Feb 13 2006 EXTENSIONS More terms from Farideh Firoozbakht, Aug 24 2006 a(22)-a(25) from Donovan Johnson, Feb 19 2013 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)