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%I #11 Feb 23 2017 02:40:23
%S 13,17,19,23,37,47,67,89,103,107,109,113,131,151,173,193,199,233,239,
%T 269,277,317,353,359,373,389,409,431,433,443,449,463,467,499,503,563,
%U 577,593,607,619,653,709,719,727,773,811,823,829,863,881,887,911,937,947,997,1033
%N Primes of the form prime(k+1) + prime(k+2) - prime(k).
%C Some terms can be obtained in more than one way.
%C For example 47 =37+41-31 = 41+43-37.
%C 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.
%H Charles R Greathouse IV, <a href="/A175873/b175873.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 = 7+11-5, 17=11+13-7
%o (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
%K nonn
%O 1,1
%A _Claudio Meller_, Dec 05 2010
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