A165698 -id:A165698 - cp's OEIS frontend

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

Farideh Firoozbakht, Apr 21 2006

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)

			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.

Cf. A118213.

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

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 *)

A165696 a(n) is the smallest number m such that the n numbers A004086(m^k) (digit reversal of m^k) for 0 < k < n+1 are all primes.

Original entry on oeis.org

2, 14, 325, 3244, 3244, 110218462, 32149366346, 10212002596432

Offset: 1

Farideh Firoozbakht, Sep 29 2009

			Both numbers A004086(14) = 41 and A004086(14^2) = 691 are primes and 14 is the smallest number with this property so a(2) = 14.

Cf. A004086, A118212, A118213, A165697, A165698, A165699.

a(8) from Matthias Baur, Mar 03 2021

A165697 a(n) is the smallest prime p such that all the n numbers reversal(p^k), k

Original entry on oeis.org

2, 37, 3121, 10429, 10282339, 9835884797, 101740496633

Offset: 1

Farideh Firoozbakht, Sep 29 2009

By an interesting approach I was able to find a(7). [From Farideh Firoozbakht, Sep 30 2009]

			Both numbers reversal(37)=73 & reversal(37^2)=9631 are primes and 37 is the
smallest prime number with this property so a(2)=37.

Cf. A118212, A118213, A165696, A165698.

a(7) from Farideh Firoozbakht, Sep 30 2009

cp's OEIS Frontend

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

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A165696 a(n) is the smallest number m such that the n numbers A004086(m^k) (digit reversal of m^k) for 0 < k < n+1 are all primes.

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A165697 a(n) is the smallest prime p such that all the n numbers reversal(p^k), k

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