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A072537 a(1) = 2, a(2) = 3 and a(n) = the smallest prime which is a linear combination of all previous terms with all coefficients >= 1.

%I A072537 #13 May 02 2019 08:50:45
%S A072537 2,3,5,13,23,53,101,211,419,839,1669,3343,6689,13381,26759,53527,
%T A072537 107053,214129,428221,856459,1712899,3425803,6851617,13703231,
%U A072537 27406471,54812957,109625881,219251761,438503537,877007063,1754014121
%N A072537 a(1) = 2, a(2) = 3 and a(n) = the smallest prime which is a linear combination of all previous terms with all coefficients >= 1.
%H A072537 Robert Israel, <a href="/A072537/b072537.txt">Table of n, a(n) for n = 1..3318</a>
%F A072537 For n >= 3, a(n) = A151800(S+(-1)^S) where S = Sum_{i=1..n-1} a(i). - _Robert Israel_, May 01 2019
%p A072537 A[1]:= 2: A[2]:= 3: S:= 5:
%p A072537 for i from 3 to 50 do
%p A072537   if S::even then A[i]:= nextprime(S+1)
%p A072537 else A[i]:= nextprime(S-1)
%p A072537   fi;
%p A072537 S:= S + A[i]
%p A072537 od:
%p A072537 seq(A[i],i=1..50); # _Robert Israel_, May 01 2019
%Y A072537 Cf. A072536, A000040, A062391, A151800.
%K A072537 nonn
%O A072537 1,1
%A A072537 _Amarnath Murthy_, Aug 03 2002
%E A072537 Corrected and extended by _Sascha Kurz_, Feb 12 2003