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Each term is the smallest prime > the sum of the previous 2 terms.
2

%I #9 Apr 14 2022 09:56:47

%S 1,1,3,5,11,17,29,47,79,127,211,347,563,911,1481,2393,3877,6271,10151,

%T 16427,26591,43019,69623,112643,182279,294923,477209,772139,1249361,

%U 2021501,3270863,5292367,8563237,13855607,22418849,36274471,58693331

%N Each term is the smallest prime > the sum of the previous 2 terms.

%H Harvey P. Dale, <a href="/A073022/b073022.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n+1)=nextprime(a(n)+a(n-1))

%e After 1,1, the next prime >2 is 3.

%t nxt[{a_,b_}]:={b,NextPrime[a+b]}; NestList[nxt,{1,1},40][[All,1]] (* _Harvey P. Dale_, Apr 14 2022 *)

%o (PARI) l=1; h=1; print1("1, 1, "); while(l<2^32,t=l+h+1; while(!isprime(t),t+=1); print1(t,", "); l=h; h=t)

%Y Cf. A055498.

%K nonn

%O 0,3

%A _Phil Carmody_, Aug 15 2002