A333425 - OEIS

%I #14 Mar 21 2020 07:13:08

%S 227,283,2339,2351,2357,2393,2767,2777,2789,2797,2801,2833,2851,2861,

%T 30059,30089,30161,30169,30187,30197,30223,30293,30313,30319,30389,

%U 30391,30449,30467,30509,30517,30559,30631,30649,30677,30689,30727,30763,30781,30803,30851

%N Primorial base emirps: prime numbers whose primorial base reversal is a different prime.

%H Amiram Eldar, <a href="/A333425/b333425.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mixed_radix#Primorial_number_system">Primorial number system</a>.

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.

%e 227 is a term since it is a prime number and its representation in primorial base is 10221, whose reversal, 12201, is the primorial base representation of another prime number, 283.

%t max = 7; bases = Prime @ Range[max, 1, -1]; nmax = Times @@ bases - 1; emirpQ[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n, MixedRadix[bases]]}, r = Reverse @ d; IntegerDigits[(m = FromDigits[r, MixedRadix[bases]]), MixedRadix[bases]] == r && m != n && PrimeQ[m]]; Select[Range[nmax], emirpQ]

%Y Cf. A049345, A235168, A333424.

%Y Cf. A006567, A080790, A333422.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 20 2020