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A236512 Primes whose representation in base (2), base (3), base (4) and base (5) are also prime when read in decimal.

%I A236512 #16 Jul 17 2025 21:45:07
%S A236512 9241,85303,110581,296011,331081,465523,644353,659371,849943,1108993,
%T A236512 1116163,1210483,2149471,2469241,2963923,3409753,3704203,4451071,
%U A236512 4774801,4978003,5665213,5674993,5995021,6507343,6817501,7529941,7596373,7693531,7973653,8320831,8344681
%N A236512 Primes whose representation in base (2), base (3), base (4) and base (5) are also prime when read in decimal.
%H A236512 K. D. Bajpai, <a href="/A236512/b236512.txt">Table of n, a(n) for n = 1..797</a>
%e A236512 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 A236512 t={}; n=1; While[Length[t]<31,n=NextPrime[n]; If[PrimeQ[FromDigits[IntegerDigits[n,2]]]&&PrimeQ[FromDigits[IntegerDigits[n,3]]] &&PrimeQ[FromDigits[IntegerDigits[n,4]]]&&PrimeQ[FromDigits[IntegerDigits[n,5]]], AppendTo[t,n]]]; t
%o A236512 (PARI)
%o A236512 default(primelimit,2^31)
%o A236512 base_b(n, b) = {
%o A236512   my(s=[], r, x=10);
%o A236512   while(n>0,
%o A236512     r = n%b;
%o A236512     n = n\b;
%o A236512     s = concat(r, s)
%o A236512   );
%o A236512   eval(Pol(s))
%o A236512 }
%o A236512 A236512(maxp) = {
%o A236512   forprime(p=2, maxp,
%o A236512     if(isprime(base_b(p, 2)) &&
%o A236512        isprime(base_b(p, 3)) &&
%o A236512        isprime(base_b(p, 4)) &&
%o A236512        isprime(base_b(p, 5)), print1(p, ", ")
%o A236512     )
%o A236512   )
%o A236512 }
%o A236512 \\ _Colin Barker_, Jan 29 2014
%Y A236512 Cf. A000040 (prime numbers), A065720 (primes: binary representation is also prime),
%Y A236512 A236365 (primes: binary and octal representation is also prime).
%K A236512 nonn,base
%O A236512 1,1
%A A236512 _K. D. Bajpai_, Jan 27 2014