login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A241757 Numbers n such that 2n is a sum of two primes, the adding of which requires only one carry in binary. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)