A230017 Prime terms in the tribonacci-like sequence, A214825.
3, 3, 7, 13, 23, 43, 79, 491, 19009, 34963, 8422747, 326099713, 3699221592878859104602113553, 77867739062209443974741001359, 63460200981504216633346603450897, 174962190954783387911511685367053207
Offset: 1
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Mathematica
a={1,3,3}; Print[3]; Print[3]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]