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

1,1

Links

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

Example

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.

Mathematica

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*)

Prog

(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

Crossrefs

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

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

Sequence in context: A272596 A189984 A092005 * A031848 A184211 A035910

Adjacent sequences: A236509 A236510 A236511 * A236513 A236514 A236515

Keyword

nonn,base

Author

K. D. Bajpai, Jan 27 2014

Status

approved