A236174 Maximal prime among the base-k representations of the n-th prime, read in decimal, for k=2,3,...,10.

2, 11, 101, 13, 23, 31, 101, 103, 10111, 131, 43, 211, 131, 223, 101111, 311, 113, 331, 2111, 1013, 1021, 2221, 1103, 1011001, 1201, 1100101, 10211, 1223, 1231, 1301, 331, 2003, 211, 12011, 10010101, 2113, 10011101, 10100011, 2213, 10101101, 10110011, 20201, 2333, 21011, 3011, 11000111, 21211, 337, 3203, 11100101

Offset: 1

Author

Vladimir Shevelev, Jan 19 2014

Keywords

• nonn
• base
• nice

Comments

Let p = n-th prime. Write p in base k, k=2,3,4,5,..., and stop when the result is a prime when looked at in base 10. - N. J. A. Sloane, Jan 25 2014

Examples

			Let n=10, then prime(n)=29 (in base 10). The representations of 29 in bases 2,3,4,...,10 are 11101,1002,131,...,29 respectively. In this list 131 is the first and therefore the maximal prime. Thus a(10)=131.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040, A052033, A235354, A235376, A235377, A236437.

Programs

Mathematica

Map[First[First[Select[Map[{#,PrimeQ[#]}&,Map[FromDigits,IntegerDigits[Prime[#],Range[2,10]]]],#[[2]]==True&]]]&,Range[50]]
Table[SelectFirst[Table[FromDigits[IntegerDigits[Prime[n],b]],{b,2,10}],PrimeQ],{n,80}] (* Harvey P. Dale, May 17 2024 *)

PARI

base_b(n, b) = {
  my(s=[], r, x);
  while(n>0,
    r = n%b;
    n = n\b;
    s = concat(r, s)
  );
  x=10;
  eval(Pol(s))
}
A236174(maxp) = {
  my(s=[], b, t);
  forprime(p=2, maxp,
    for(b=2, 10,
      t=base_b(p, b);
      if(isprime(t), s=concat(s, t); break)
    )
  );
  s
} \\ Colin Barker, Jan 23 2014

Python

from sympy import prime, isprime
def A236174(n):
    p = prime(n)
    for b in range(2,11):
        x, y, z = p, 0, 1
        while x >= b:
            x, r = divmod(x,b)
            y += r*z
            z *= 10
        y += x*z
        if isprime(y):
            return y # Chai Wah Wu, Jan 03 2015