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 A175873 Primes of the form prime(k+1) + prime(k+2) - prime(k). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 13 = 7+11-5, 17=11+13-7 PROG (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 CROSSREFS Sequence in context: A165681 A214033 A268593 * A167802 A105878 A054476 Adjacent sequences:  A175870 A175871 A175872 * A175874 A175875 A175876 KEYWORD nonn AUTHOR Claudio Meller, Dec 05 2010 STATUS approved

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Last modified January 22 08:40 EST 2021. Contains 340360 sequences. (Running on oeis4.)