%N Smallest positive prime number such that a(n)-2n is also prime, a(n) < a(n+1), and the differences a(n)-2n must increase with n.
%C Subtracting from a(1) twice n=1 gives 5-2=3, which is a prime number; subtracting from a(2) twice n=2 gives 11-4=7, which is a prime number; subtracting from a(3) twice n=3 gives 17-6=11, which is a prime number; subtracting from a(4) twice n=4 gives 31-8=23, which is a prime number; etc.
%H Alois P. Heinz, <a href="/A155882/b155882.txt">Table of n, a(n) for n = 1..1000</a>
%p b:= proc(n) option remember; global a; a(n); b(n) end: a:= proc(n) option remember; local m; global b; if n=1 then b(1):= 3; 5 else for m from a(n-1)+2 by 2 while not (isprime(m) and (b(n-1)<m-2*n) and isprime (m-2*n)) do od; b(n):= m-2*n; m fi end: seq (a(n), n=1..100); # _Alois P. Heinz_, Feb 05 2009
%Y Cf. A020484, A108184 (for the differences a(n)-2n).
%A _Eric Angelini_, Jan 29 2009
%E Corrected definition and more terms from _Alois P. Heinz_, Feb 05 2009