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Primes whose representation in base (2), base (3), base (4) and base (5) are also prime when read in decimal.
2

%I #13 Jan 29 2014 14:03:22

%S 9241,85303,110581,296011,331081,465523,644353,659371,849943,1108993,

%T 1116163,1210483,2149471,2469241,2963923,3409753,3704203,4451071,

%U 4774801,4978003,5665213,5674993,5995021,6507343,6817501,7529941,7596373,7693531,7973653,8320831,8344681

%N Primes whose representation in base (2), base (3), base (4) and base (5) are also prime when read in decimal.

%H K. D. Bajpai, <a href="/A236512/b236512.txt">Table of n, a(n) for n = 1..797</a>

%e 9241 is in the sequence because it is prime. Its representation in base (2):{10010000011001}, base (3):{110200021}, base (4):{2100121} and base (5):{243431}, when read in decimal are also prime.

%t t={}; n=1; While[Length[t]<100,n=NextPrime[n]; If[PrimeQ[FromDigits[IntegerDigits[n,2]]]&&PrimeQ[FromDigits[IntegerDigits[n,3]]] &&PrimeQ[FromDigits[IntegerDigits[n,4]]]&&PrimeQ[FromDigits[IntegerDigits[n,5]]], ApendTo[t,n]]] t (*_K. D. Bajpai_*)

%o (PARI)

%o default(primelimit,2^31)

%o base_b(n, b) = {

%o my(s=[], r, x=10);

%o while(n>0,

%o r = n%b;

%o n = n\b;

%o s = concat(r, s)

%o );

%o eval(Pol(s))

%o }

%o A236512(maxp) = {

%o forprime(p=2, maxp,

%o if(isprime(base_b(p, 2)) &&

%o isprime(base_b(p, 3)) &&

%o isprime(base_b(p, 4)) &&

%o isprime(base_b(p, 5)), print1(p, ", ")

%o )

%o )

%o }

%o \\ _Colin Barker_, Jan 29 2014

%Y Cf. A000040 (prime numbers), A065720 (primes: binary representation is also prime),

%Y A236365 (primes: binary and octal representation is also prime).

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 27 2014