%I #15 Feb 20 2014 03:13:48
%S 3,5,7,11,17,23,29,41,53,83,113,173,233,293,353,593,953,1553,2153,
%T 2753,5153,8753,14753,20753,36353,71153,105953,211313,419873,733793,
%U 1047713,2086673,4102193,8133233,14179793,26272913,52439873,90699953,128960033,167220113
%N Starting with a(1) = 3, a(2) = 5, a(n+1) is the smallest prime number greater than the previous term a(n) such that there exists k satisfying 1<=k<n, a(n+1) = 2*a(n) - a(k).
%C This sequence is finite. - _Alois P. Heinz_, Feb 19 2014
%H Alois P. Heinz, <a href="/A238137/b238137.txt">Table of n, a(n) for n = 1..312</a>
%e a(1) = 3, a(2) = 5, a(3) = 2*5 - 3 = 7, a(4) = 2*7 - 3 = 11, a(5) = 2*11 - 5 = 17, ...
%p a:= proc(n) a(n):= `if`(n<3, [3, 5][n], min(select(p->p>a(n-1)
%p and isprime(p), {seq(2*a(n-1)-a(k), k=1..n-2)})[]))
%p end:
%p seq(a(n), n=1..45); # _Alois P. Heinz_, Feb 19 2014
%Y Cf. A000040.
%K nonn,fini,full
%O 1,1
%A _Philippe Deléham_, Feb 18 2014
%E More terms from _Alois P. Heinz_, Feb 19 2014