A175873 Primes of the form prime(k+1) + prime(k+2) - prime(k).

13, 17, 19, 23, 37, 47, 67, 89, 103, 107, 109, 113, 131, 151, 173, 193, 199, 233, 239, 269, 277, 317, 353, 359, 373, 389, 409, 431, 433, 443, 449, 463, 467, 499, 503, 563, 577, 593, 607, 619, 653, 709, 719, 727, 773, 811, 823, 829, 863, 881, 887, 911, 937, 947, 997, 1033

Offset: 1

Author

Claudio Meller, Dec 05 2010

Keywords

• nonn

Comments

Some terms can be obtained in more than one way.

For example 47 =37+41-31 = 41+43-37.

The formula in the definition adds a previous prime gap prime(k+1)-prime(k) to the prime(k+2); the gap is basically >=2, so there is a minimal growth which yields safe bounds to algorithms.

Examples

			13 = 7+11-5, 17=11+13-7
		

Links

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

Programs

PARI

list(lim)=my(v=List(),t,p=2,q=3); forprime(r=5,lim-2, t=q+r-p; if(isprime(t) && t<=lim, listput(v,t)); p=q; q=r); Set(v) \\ Charles R Greathouse IV, Feb 23 2017