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A068524 a(1) = 2; for n > 1, a(n) = largest prime not exceeding a(1) + ... + a(n-1).

%I A068524 #19 Aug 09 2025 07:47:38
%S A068524 2,2,3,7,13,23,47,97,193,383,769,1531,3067,6133,12269,24533,49069,
%T A068524 98129,196247,392503,785017,1570007,3140041,6280067,12560147,25120289,
%U A068524 50240587,100481167,200962327,401924639,803849303,1607698583,3215397193,6430794373,12861588749
%N A068524 a(1) = 2; for n > 1, a(n) = largest prime not exceeding a(1) + ... + a(n-1).
%H A068524 Robert Israel, <a href="/A068524/b068524.txt">Table of n, a(n) for n = 1..2000</a>
%e A068524 a(4) = largest prime not exceeding a(3) + a(2) + a(1) = 3 + 2 + 2 = 7; so a(4) = 7.
%p A068524 A[1]:= 2: S:= 2:
%p A068524 for n from 2 to 100 do
%p A068524   A[n]:= prevprime(S+1);
%p A068524   S:= S + A[n];
%p A068524 od:
%p A068524 seq(A[i],i=1..100); # _Robert Israel_, Jul 08 2020
%t A068524 s={2};ss=2;Do[a=If[PrimeQ[ss], ss, Prime[PrimePi[ss]]];AppendTo[s, a];AddTo[ss, a], {i, 40}];A068524=s (* _Zak Seidov_, Sep 10 2005 *)
%o A068524 (PARI) /* Version 2.1.5 of PARI uses Pocklington-Lehmer to certify primality */ /* of a_n when 1 is used as the optional flag in isprime: isprime(a_n,1) */ {a1=2; a2=2; print1(a1,",",a2,","); s=a1+a2; for(n=3,40, a_n=precprime(s); if(isprime(a_n,1), print1(a_n,","); s=s+a_n, error("very unlikely event occurred: ",a_n, " is a strong pseudoprime to up to 10 randomly-chosen bases but is not prime")))} \\ _Rick L. Shepherd_, Jun 15 2004
%K A068524 nonn
%O A068524 1,1
%A A068524 _Joseph L. Pe_, Mar 21 2002
%E A068524 More terms from _Rick L. Shepherd_, Jun 15 2004