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 A085331 Numbers n such that phi(rev(n))=n. 6
 1, 12, 36, 192, 1992, 2016, 31067664, 39206496, 1564356432, 3937403136, 15600000432, 22871605008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS rev(2*(10^k-4)) = 3*(10^k-3). If 10^k-3 is prime, then phi(3*(10^k-3)) = 2*(10^k-4), so 2*(10^k-4) is a term. 10^1-3=7 is prime, so 2*(10^1-4)=12 is a term, a(2). 10^2-3=97 is prime, so 2*(10^2-4)=192 is a term, a(4). 10^3-3=997 is prime, so 2*(10^3-4)=1992 is a term, a(5). 10^17-3 is prime, so 2*(10^17-4)=199999999999999992 is a term. 10^140-3 is prime, so 2*(10^140-4) is a term. 10^990-3 is prime, so 2*(10^990-4) is a term. Conjecture: sequence is infinite. - Ray Chandler, Jul 20 2003 Let f(m,n,r,t)=((9).(m).78.(0)(n).21.(9)(m))(r).(9)(t).7 where m, n, r & t are nonnegative integers; dot between numbers means concatenation and "(m)(n)" means number of m's is n. If r*t=0 & p=f(m,n,r,t) is prime then reversal(3*p) = 1.((9)(m).56.(0)(n).43.(9)(m))(r).(9)(t).2 is in the sequence. For example p1=f(0,0,0,0)=7 so reversal(3*p1) = 12 is in the sequence, p2=f(0,0,2,0)=(7821)(2).7=782178217 so reversal(3*p2) = 1.(5643)(2).2 = 1564356432 is in the sequence & p3=f(0,0,674,0) so reversal(3*p3) = 1.(5643)(674).2 is in the sequence. Primes of the form f(m,n,r,t) are a generalized form of primes of the form 10^j-3 that were already related to this sequence by Ray Chandler. For all n, A085331(n) = reversal(A072395(n)). - Farideh Firoozbakht, Jan 08 2005 The list is complete through 2050000000. - Farideh Firoozbakht, Jan 15 2005 a(13) > 10^11. - Donovan Johnson, Feb 03 2012 LINKS EXAMPLE phi[{1,21,63,291,2991,6102}] = {1,12,36,192,1992,2016} MATHEMATICA v = {1}; Do[ If[ n == EulerPhi[ FromDigits[ Reverse[ IntegerDigits [ n ] ] ] ], v = Append[ v, n ]; Print[ v ], If[ Mod[ n, 1000000 ] == 0, Print[ -n ] ] ], {n, 2, 2050000000, 2} ] (Firoozbakht) CROSSREFS Cf. A000010, A004086, A069215, A101700, A102278. Sequence in context: A135178 A278583 A216381 * A225100 A058040 A130164 Adjacent sequences:  A085328 A085329 A085330 * A085332 A085333 A085334 KEYWORD base,nonn AUTHOR Labos Elemer, Jul 04 2003 EXTENSIONS The terms 31067664, 39206496, 1564356432 are from Farideh Firoozbakht, Jan 08 2005 a(10)-a(12) from Donovan Johnson, Feb 03 2012 STATUS approved

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Last modified May 26 05:25 EDT 2019. Contains 323579 sequences. (Running on oeis4.)