Search: id:A069217
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%I A069217
%S A069217 1,2,3,5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919,
%T A069217 929,10301,10501,10601,11311,11411,12421,12721,12821,13331,13831,13931,
%U A069217 14341,14741,15451,15551,16061,16361,16561,16661,17471,17971,18181
%N A069217 Numbers n such that phi(n) + sigma(n) = n + reversal(n).
%C A069217 Note that all terms so far are palindromes.
%C A069217 It is obvious that if n is a term of the sequence greater than 1 then 
               n is prime iff n is a palindrome. Do there exist composite terms 
               in the sequence? - Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               Jan 28 2006 Answer: Yes, see next comment.
%C A069217 Giovanni Resta writes (Sep 06 2006): The smallest composite number such 
               that n+rev(n)=phi(n)+sigma(n) is n = 3197267223 = 3 * 79 * 677 * 
               19927 with rev(n) = 3227627913, phi(n) = 2101316256, sigma(n) = 4323578880 
               and 3197267223+3227627913 = 6424895136 = 2101316256+4323578880.
%F A069217 If p is prime and rev(p)=p then p+rev(p)=2p=phi(p)+sigma(p) so all palindromic 
               primes are in the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               Sep 12 2006
%e A069217 phi(101) + sigma(101) = 202 = 101 + 101 = 101 + reversal(101).
%t A069217 Select[Range[5*10^4], EulerPhi[ # ] + DivisorSigma[1, # ] == # + FromDigits[Reverse[IntegerDigits[ 
               # ]]] &]
%Y A069217 Contains composite terms, so is strictly different from A002385.
%Y A069217 Sequence in context: A083137 A077652 A002385 this_sequence A083139 A088562 
               A083712
%Y A069217 Adjacent sequences: A069214 A069215 A069216 this_sequence A069218 A069219 
               A069220
%K A069217 base,nonn
%O A069217 1,2
%A A069217 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 11 2002

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