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A214415 Numbers n such that prevprime(2^n) AND nextprime(2^n) = 1, where AND is the bitwise AND operator. 2
2, 4, 6, 8, 12, 15, 16, 23, 25, 30, 37, 53, 55, 57, 67, 75, 76, 81, 82, 84, 95, 108, 129, 132, 135, 139, 143, 155, 160, 163, 180, 181, 188, 192, 203, 204, 210, 222, 244, 263, 273, 277, 280, 287, 289, 295, 297, 308, 315, 319, 325, 330, 341, 367, 370, 393, 394, 406 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A007053(a(n)) are indices of 1's in A175330. That is, A175330(A007053(a(n)))=1.

Conjecture: the sequence is infinite.

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

4 is in the sequence because (prevprime(2^4) AND nextprime(2^4)) = 13 AND 17 = 1.

MATHEMATICA

ba1Q[n_]:=Module[{c=2^n}, BitAnd[NextPrime[c], NextPrime[c, -1]]==1]; Select[ Range[ 450], ba1Q] (* Harvey P. Dale, Dec 25 2012 *)

PROG

(Java)

import java.math.BigInteger;

public class A214415 {

  public static void main (String[] args) {

    BigInteger b1 = BigInteger.valueOf(1);

    BigInteger b2 = BigInteger.valueOf(2);

    for (int n=2; ; n++) {

      BigInteger pwr = b1.shiftLeft(n);

      BigInteger pm  = pwr.subtract(b1);

      BigInteger pp  = pwr.add(b1);

      while (true) {

        if (pm.isProbablePrime(2)) {

            if (pm.isProbablePrime(80)) break;

        }

        pm  = pm.subtract(b2);

      }

      while (true) {

        if (pp.isProbablePrime(2)) {

            if (pp.isProbablePrime(80)) break;

        }

        pp  = pp.add(b2);

      }

      if (pm.and(pp).equals(b1)) {

        System.out.printf("%d, ", n);

      }

    }

  }

}

(PARI)

{ for (n=2, 1000,  N = 2^n;

    p1 = precprime(N-1);

    p2 = nextprime(N+1);

    ba = bitand(p1, p2);

    if ( bitand( ba, ba-1 ) == 0, print1(n, ", "));

); }

/* Joerg Arndt, Aug 16 2012 */

CROSSREFS

Cf. A007053, A175330.

Sequence in context: A082742 A131197 A078327 * A094109 A090404 A015937

Adjacent sequences:  A214412 A214413 A214414 * A214416 A214417 A214418

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Aug 07 2012

STATUS

approved

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Last modified December 11 02:20 EST 2019. Contains 329910 sequences. (Running on oeis4.)