cp's OEIS Frontend

A232239 Lesser of twin-bin primes: primes p such that p+2, x and y are primes, where x is concatenation of binary representations of p and p+2, and y is concatenation of binary representations of p+2 and p: x = p * 2^A070939(p+2) + p+2, y = (p+2) * 2^A070939(p) + p.

%I A232239 #23 Jan 26 2014 14:31:17
%S A232239 3,5,269,16649,27689,29129,82889,93239,129629,274199,289169,309479,
%T A232239 336899,349079,371339,374639,415109,454709,463889,492719,1051079,
%U A232239 1063919,1127309,1198289,1209779,1229519,1268789,1350959,1354649,1355279,1392539,1430879,1547129,1551959
%N A232239 Lesser of twin-bin primes: primes p such that p+2, x and y are primes, where x is concatenation of binary representations of p and p+2, and y is concatenation of binary representations of p+2 and p: x = p * 2^A070939(p+2) + p+2, y = (p+2) * 2^A070939(p) + p.
%C A232239 Conjecture: the sequence is infinite.
%e A232239 269 is in the sequence because the following are three primes: 271, 269 * 512 + 271 = 137999, 271 * 512 + 269 = 139021.
%t A232239 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 *)
%o A232239 (Java)
%o A232239 import java.math.BigInteger;
%o A232239 public class A232239 {
%o A232239 public static void main (String[] args) {
%o A232239 long bl = 2, next = 3; // bit length, next n such that bl++ for n + 2
%o A232239 for (long n = 3; n < 0xffffffffL; n += 2) {
%o A232239   long blPrev = bl;
%o A232239   if (n == next) { ++bl; next = next * 2 + 1; }
%o A232239   if (BigInteger.valueOf(n).isProbablePrime(80) &&
%o A232239     BigInteger.valueOf(n + 2).isProbablePrime(80) &&
%o A232239     BigInteger.valueOf((n << bl) + n + 2).isProbablePrime(80) &&
%o A232239     BigInteger.valueOf(((n + 2) << blPrev) + n).isProbablePrime(80))
%o A232239         System.out.printf("%d, ", n);
%o A232239 }
%o A232239 }
%o A232239 }
%Y A232239 Cf. A001359, A070939, A232237, A232238.
%K A232239 nonn,base,less
%O A232239 1,1
%A A232239 _Alex Ratushnyak_, Nov 20 2013