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a(1) = 2. a(n) = a(n-1)*(largest prime occurring earlier in the sequence) + 1.
2

%I #10 Apr 14 2023 12:18:38

%S 2,5,26,131,17162,2248223,5054506657730,11363658121561713791,

%T 25548037553031840864343394,57437685631589904363556698288863,

%U 129132725903709949557948530897082440450

%N a(1) = 2. a(n) = a(n-1)*(largest prime occurring earlier in the sequence) + 1.

%H Harvey P. Dale, <a href="/A120762/b120762.txt">Table of n, a(n) for n = 1..29</a>

%e Among the first 3 terms of the sequence, 5 is the largest prime. So a(4) = a(3)*5 +1 = 26*5 + 1 = 131.

%t nxt[{lp_,a_}]:=Module[{c=a lp+1},{If[PrimeQ[c]&&c>lp,c,lp],c}]; NestList[nxt,{2,2},12][[;;,2]] (* _Harvey P. Dale_, Apr 14 2023 *)

%o (PARI) {m=11;print1(a=2,",");v=[a];for(n=2,m,b=a;v=vecsort(v);j=#v;a=0;while(a<1,k=v[j];if(isprime(k),print1(a=b*k+1,",");v=concat(v,a),j--)))} - (Klaus Brockhaus, Aug 17 2006)

%Y Cf. A120763.

%K nonn

%O 1,1

%A _Leroy Quet_, Jul 03 2006

%E More terms from _Klaus Brockhaus_, Aug 17 2006