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

9241, 85303, 110581, 296011, 331081, 465523, 644353, 659371, 849943, 1108993, 1116163, 1210483, 2149471, 2469241, 2963923, 3409753, 3704203, 4451071, 4774801, 4978003, 5665213, 5674993, 5995021, 6507343, 6817501, 7529941, 7596373, 7693531, 7973653, 8320831, 8344681

Offset: 1

Author

K. D. Bajpai, Jan 27 2014

Keywords

• nonn
• base

Examples

			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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..797

Crossrefs

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

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

Programs

Mathematica

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

PARI

default(primelimit,2^31)
base_b(n, b) = {
  my(s=[], r, x=10);
  while(n>0,
    r = n%b;
    n = n\b;
    s = concat(r, s)
  );
  eval(Pol(s))
}
A236512(maxp) = {
  forprime(p=2, maxp,
    if(isprime(base_b(p, 2)) &&
       isprime(base_b(p, 3)) &&
       isprime(base_b(p, 4)) &&
       isprime(base_b(p, 5)), print1(p, ", ")
    )
  )
}
\\ Colin Barker, Jan 29 2014