OFFSET
1,1
COMMENTS
Conjecture: the sequence is infinite.
EXAMPLE
269 is in the sequence because the following are three primes: 271, 269 * 512 + 271 = 137999, 271 * 512 + 269 = 139021.
MATHEMATICA
Select[Prime[Range[200]], PrimeQ[# + 2] && PrimeQ[FromDigits[Flatten[{IntegerDigits[#, 2], IntegerDigits[# + 2, 2]}], 2]] && PrimeQ[FromDigits[Flatten[{IntegerDigits[# + 2, 2], IntegerDigits[#, 2]}], 2]] &] (* Alonso del Arte, Jan 19 2014 *)
PROG
(Java)
import java.math.BigInteger;
public class A232239 {
public static void main (String[] args) {
long bl = 2, next = 3; // bit length, next n such that bl++ for n + 2
for (long n = 3; n < 0xffffffffL; n += 2) {
long blPrev = bl;
if (n == next) { ++bl; next = next * 2 + 1; }
if (BigInteger.valueOf(n).isProbablePrime(80) &&
BigInteger.valueOf(n + 2).isProbablePrime(80) &&
BigInteger.valueOf((n << bl) + n + 2).isProbablePrime(80) &&
BigInteger.valueOf(((n + 2) << blPrev) + n).isProbablePrime(80))
System.out.printf("%d, ", n);
}
}
}
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Alex Ratushnyak, Nov 20 2013
STATUS
approved