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

1,1

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A241405.

Sequence in context: A255370 A061845 A297836 * A272883 A257283 A091211

Adjacent sequences: A241754 A241755 A241756 * A241758 A241759 A241760

Keyword

nonn

Author

Vladimir Shevelev, Apr 28 2014

Extensions

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

Status

approved