Search: id:A116018
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%I A116018
%S A116018 1,2,3,4,5,6,17,21,63,167,201,389,603,1667,3795,3889,4465,5926,50394,
%T A116018 166667,510042,2000001,3888889,5185194,5798663,5925926,6000003,32050435,
%U A116018 200000001,335447667,365110755,444766346,600000003,1558138862
%N A116018 Numbers n such that n + phi(n) is a repdigit.
%C A116018 (I). If p=(2*10^(3n+1)+7)/27 is prime then m=2p is in the sequence because 
               m+phi(m)=3p-1=2*(10^(3n+1)-1)/9 is a repdigit number. m=2*(2*10^811+7)/
               27 (a 811-digit number) is the smallest such terms and the next such 
               terms has 4219 digits. - Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               Aug 24 2006
%C A116018 (II). If p=(8*10^(3n+1)+1)/27 is prime then m=2p is in the sequence because 
               m+phi(m)=8*(10^(3n+1)-1)/9 is a repdigit number. 5926 is the smallest 
               such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 
               2006
%C A116018 (III). If p=(2*10^n+1)/3 then both numbers 3p & 9p are in the sequence 
               because 3p+phi(3p)=5p-2=3*(10^(n+1)-1)/9 & 9p+ phi(9p)=9*(10^(n+1)-1)/
               9 are repdigit numbers. 21 & 63 are the smallest such terms. - Farideh 
               Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
%C A116018 (IV). All primes p of the form (35*10^n+1)/9 are in the sequence because 
               p+phi(p)=7*(10^n-1)/9 is a repdigit number. 389 is the smallest such 
               terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006
%C A116018 (V). All primes p of the form (10^n+2)/6 are in the sequence because 
               p+phi(p)=2p-1=3*(10^n-1)/9 is a repdigit number. 2, 17 & 167 are 
               such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 
               2006, Dec 19 2007
%e A116018 5185194+phi(5185194)=6666666.
%Y A116018 Cf. A116017.
%Y A116018 Sequence in context: A166098 A124365 A115896 this_sequence A048095 A031015 
               A024639
%Y A116018 Adjacent sequences: A116015 A116016 A116017 this_sequence A116019 A116020 
               A116021
%K A116018 nonn,base
%O A116018 1,2
%A A116018 Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006
%E A116018 More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 
               2006

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