OFFSET
1,2
COMMENTS
For an arithmetical function f, call the arguments n such that f(reverse(n)) = reverse(f(n)) the "palinpoints" of f. This sequence is the sequence of palinpoints of f(n) = phi(n).
If n is in the sequence and 10 divides n then for each natural number m, 10^m*n is in the sequence because phi(reversal(10^m*n))=phi(reversal(n))=reversal(phi(n)) =reversal(10^m*phi(n))=reversal(phi(10^m*n)). This sequence is infinite because the numbers 2110,13580,82770,8415570 are in the sequence and according to the above assertion all numbers of the form 2110*10^m, 13580*10^m, 82770*10^m & 8415570*10^m are in the sequence. If n is in the sequence and 10 doesn't divide n then it is obvious that the reversal of n is also in the sequence. If both numbers 5*10^(n-1)-1 & 7*10^n-9 are prime we can easily show that 7*10^n-9 is in the sequence. - Farideh Firoozbakht, Jan 18 2006
If both numbers 49*10^n-9 & 125*10^(n-2)-1 are prime then 49*10^n-9 is in the sequence (the proof is easy). 3 is the only known number n such that both numbers 49*10^n-9 & 125*10^(n-2)-1 are primes. - Farideh Firoozbakht, Jan 26 2006
EXAMPLE
Let f(n) = phi(n). Then f(6188) = 2304, f(8816) = 4032, so f(reverse(6188)) = reverse(f(6188)). Therefore 6188 belongs to the sequence.
MATHEMATICA
rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; f[n_] := EulerPhi[n]; Select[Range[10^6], f[rev[ # ]] == rev[f[ # ]] &]
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Joseph L. Pe, Apr 15 2002
EXTENSIONS
More terms from Farideh Firoozbakht, Jan 18 2006
STATUS
approved