A118212 Numbers n such that the reversal of all five numbers n^1, n^2, n^3 n^4 and n^5 are primes.

3244, 32440, 324400, 324886, 1109311, 1979137, 3244000, 3248860, 10212316, 10255493, 10282339, 10306511, 10503781, 10573126, 10657861, 10692107, 11093110, 11145841, 11171452, 19791370, 19855967, 19875058, 19912073

Offset

1,1

Comments

This sequence is infinite because if n is in the sequence then for all natural numbers m, 10^m*n is in the sequence.

Contribution from Farideh Firoozbakht, Sep 29 2009: (Start)

110218462 is the smallest term n such that the reversal of n^6 is also prime.

A165698 is a subsequence of this sequence such that for each term n reversal(n^6)

is also prime. (End)

Links

Table of n, a(n) for n=1..23.

Example

3244 is in the sequence because reversal(3244^k) for k=1,2,...,5
are respectively 4423, 63532501, 48705383143, 692349908447011,
and 422250654361652953 and these five numbers are primes.

Mathematica

Do[If[PrimeQ[FromDigits[Reverse[IntegerDigits[n]]]] && PrimeQ[FromDigits[Reverse[IntegerDigits[n^2]]]] && PrimeQ [FromDigits[Reverse[IntegerDigits[n^3]]]] && PrimeQ[FromDigits [Reverse[IntegerDigits[n^4]]]] && PrimeQ[FromDigits[Reverse [IntegerDigits[n^5]]]], Print[n]], {n, 32000000}]
Select[Range[20000000], And@@PrimeQ[FromDigits[Reverse[ IntegerDigits[ #]]]&/@ (#^Range[5])]&] (* Harvey P. Dale, Jan 17 2014 *)

Crossrefs

Cf. A118213.

Cf. A165698. [From Farideh Firoozbakht, Sep 29 2009]

Sequence in context: A361262 A185465 A254974 * A233750 A252014 A247725

Adjacent sequences: A118209 A118210 A118211 * A118213 A118214 A118215

Keyword

base,easy,nonn

Author

Farideh Firoozbakht, Apr 21 2006

Status

approved