A097648 a(n) is the least non-palindromic number m such that phi(m)=phi(reversal(m))=4*10^(n+2), or 0 if no such number exists.

10040, 110440, 1014040, 11154440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Farideh Firoozbakht, Sep 04 2004

Keywords

• base
• nonn
• more

Comments

It seems that 10 divides all terms of this sequence.

Examples

			a(4)=11154440 because phi(11154440)=phi(04445111)=4000000 and 11154440 is the earliest non-palindromic number with this property.
		

Links

• C. Rivera, f(p)=f(p') , puzzle 282

Crossrefs

Subsequence of A097647.

Programs

Mathematica

a[n_]:=(For[m=4*10^(n+2), !(m!=FromDigits[Reverse[IntegerDigits[m]]] &&EulerPhi[m]==EulerPhi[FromDigits[Reverse[IntegerDigits [m]]]]==4*10^(n+2)), m++ ];m);Do[Print[a[n]], {n, 4}]

Formula

a[n_]:=(For[m=4*10^(n+2), !(m!=FromDigits[Reverse[IntegerDigits[m]]] &&EulerPhi[m]==EulerPhi[FromDigits[Reverse[IntegerDigits [m]]]]==4*10^(n+2)), m++ ];m)

Extensions

Better definition and more terms from David Wasserman, Dec 28 2007

a(27)-a(49) from Max Alekseyev, Oct 17 2008; Aug 15 2013; Jun 14 2022