A241757 - OEIS

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

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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))

);

}; \\ Charles R Greathouse IV, Apr 30 2014

CROSSREFS

Cf. A241405.

Sequence in context: A255370 A061845 A297836 * A377473 A272883 A257283