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

2, 2, 3, 7, 13, 23, 47, 97, 193, 383, 769, 1531, 3067, 6133, 12269, 24533, 49069, 98129, 196247, 392503, 785017, 1570007, 3140041, 6280067, 12560147, 25120289, 50240587, 100481167, 200962327, 401924639, 803849303, 1607698583, 3215397193, 6430794373, 12861588749

Offset: 1

Author

Joseph L. Pe, Mar 21 2002

Keywords

• nonn

Examples

			a(4) = largest prime not exceeding a(3) + a(2) + a(1) = 3 + 2 + 2 = 7; so a(4) = 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Programs

Maple

A[1]:= 2: S:= 2:
for n from 2 to 100 do
  A[n]:= prevprime(S+1);
  S:= S + A[n];
od:
seq(A[i],i=1..100); # Robert Israel, Jul 08 2020

Mathematica

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 *)

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

Extensions

More terms from Rick L. Shepherd, Jun 15 2004