A241757 Numbers n such that 2n is a sum of two primes, the adding of which requires only one carry in binary.

2, 11, 15, 23, 27, 29, 39, 45, 47, 51, 55, 57, 59, 63, 71, 77, 87, 95, 99, 103, 105, 107, 111, 115, 117, 119, 123, 125, 127, 131, 135, 137, 143, 147, 149, 155, 159, 165, 171, 173, 175, 177, 179, 183, 185, 187, 189, 191, 197, 203, 207, 215, 219, 221, 223, 225

Offset: 1

Author

Vladimir Shevelev, Apr 28 2014

Keywords

• nonn

Comments

Apart from a(1), both primes are 1 mod 4, hence 2 is the only even term in the sequence. - Charles R Greathouse IV, Apr 29 2014

Examples

			2 is in the sequence since 2*2=2+2 is a sum of two primes and adding 2+2 requires only one carry in binary.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A241405.

Programs

PARI

is(n)=if(n%2==0, return(n==2)); forprime(p=2,n,if(p%4==1 && isprime(2*n-p) && bitand(p, 2*n-p)==1, return(1))); 0 \\ Charles R Greathouse IV, Apr 29 2014

PARI

MSB(n)=2^(#binary(n)-1);
is(n)={
    if(n%2==0, return(n==2));
    my(V=(n - MSB(n))>>1, k=0);
    while(k=bitand(k-V,V),    \\ Note: assignment, not comparison
        my(p=4*k+1,q=2*n-p);
        if(isprime(p) && isprime(q), return(1))
    );
    0
}; \\ Charles R Greathouse IV, Apr 30 2014

Extensions

More terms from Peter J. C. Moses, Apr 29 2014