

A097647


Nonpalindromic numbers n such that phi(n) = phi(reversal(n)).


6



190, 427, 429, 724, 924, 4147, 4697, 6276, 6726, 7414, 7964, 9079, 9709, 10040, 10940, 14450, 15860, 19190, 20493, 20553, 28092, 28215, 29082, 35502, 39402, 41847, 42777, 44629, 46899, 49929, 51282, 51845, 53075, 54815, 57035, 57677
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OFFSET

1,1


COMMENTS

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?
(190/99)*(100^m1) 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]
There are no prime terms < 10^10.  Donovan Johnson, Oct 18 2013


LINKS

Table of n, a(n) for n=1..36.


EXAMPLE

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


MAPLE

with(numtheory);
A097647:=proc(q)
local a, b, n;
for n from 1 to q do
a:=n; b:=0; while a>0 do b:=b*10+(a mod 10); a:=trunc(a/10); od;
if n<>b then if phi(n)=phi(b) then print(n); fi; fi; od; end:
A097647 (1000000); # Paolo P. Lava, Jan 07 2013.


MATHEMATICA

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


CROSSREFS

Cf. A097648, A085329.
Cf. A001651, A229903.
Sequence in context: A218292 A333834 A051979 * A248995 A258725 A232387
Adjacent sequences: A097644 A097645 A097646 * A097648 A097649 A097650


KEYWORD

base,nonn


AUTHOR

Farideh Firoozbakht, Aug 28 2004


STATUS

approved



