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

1,1

Comments

It seems that 10 divides all terms of this sequence.

Links

Table of n, a(n) for n=1..49.

C. Rivera, f(p)=f(p') , puzzle 282

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)

Example

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

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}]

Crossrefs

Subsequence of A097647.

Sequence in context: A251136 A213318 A346026 * A188663 A250711 A223431

Adjacent sequences: A097645 A097646 A097647 * A097649 A097650 A097651

Keyword

base,nonn,more

Author

Farideh Firoozbakht, Sep 04 2004

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

Status

approved