A097647 - OEIS

%I #27 Feb 23 2024 07:29:03

%S 190,427,429,724,924,4147,4697,6276,6726,7414,7964,9079,9709,10040,

%T 10940,14450,15860,19190,20493,20553,28092,28215,29082,35502,39402,

%U 41847,42777,44629,46899,49929,51282,51845,53075,54815,57035,57677

%N Non-palindromic numbers n such that phi(n) = phi(reversal(n)).

%C If n is in the sequence and 10 doesn't divide n then reversal(n) is also in the sequence. There exists three terms of this sequence less than 180000000 that reversal of them are primes,i.e. 10040,14450 and 1865170. This sequence has 445 composite terms less than 20000000 and there is no prime term up to 222000000. Has this sequence at least one prime term?

%C (190/99)*(100^m-1) is in the sequence iff 3 does not divide m (m is a term of A001651). So the sequence is infinite. A229903: 190, 19190, 191919190, 19191919190, ...  are such terms. [_Jahangeer Kholdi_, Oct 17 2013]

%C There are no prime terms < 10^10. - _Donovan Johnson_, Oct 18 2013

%e 10040 is in the sequence because phi(10040)=phi(4001)=4000.

%t Do[If[n!=FromDigits[Reverse[IntegerDigits[n]]]&&EulerPhi[n]==EulerPhi[ FromDigits[Reverse[IntegerDigits[n]]]], Print[n]], {n, 80000}]

%Y Cf. A097648, A085329.

%Y Cf. A001651, A229903.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Aug 28 2004