A243159 Number of primes whose binary representation has length n and which translates ('inter-base translation') to ternary as a prime.

0, 1, 1, 2, 0, 2, 5, 11, 6, 28, 39, 57, 96, 163, 324, 486, 967, 1493, 2915, 5083, 9343, 16836, 31877, 55587, 105785, 189879, 357614, 664588, 1257356, 2254304, 4303412, 8113964, 15259583, 28364673

Offset

1,4

Links

Table of n, a(n) for n=1..34.

Example

The only binary 5-digit (-bit) primes are decimal 17, 19, 23, 29 and 31; and reading the binary representations of these as base-3 representations instead produces numbers whose decimal representations are 82, 85, 94, 118 and 121.  None of these 5 numbers are prime, so a(5)=0.

Prog

(PARI)
{
i=1; while(1,
  z=0; forprime(p=2^(i-1), 2^i-1,
    b=binary(p); u=0; for(j=1, i,
      if(b[j], u+=3^(i-j))); if(isprime(u), z++));
  print1(z", "); i++)
}

Crossrefs

Cf. A235266.

Sequence in context: A256488 A175631 A243816 * A339327 A258144 A113772

Adjacent sequences: A243156 A243157 A243158 * A243160 A243161 A243162

Keyword

nonn,base

Author

James G. Merickel, May 31 2014

Status

approved