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A126273 a(0) = a(1) = a(2) = 1, a(n) = largest prime <= a(n-1) + a(n-2) + a(n-3).

%I A126273 #8 Jun 16 2021 14:36:23
%S A126273 1,1,1,3,5,7,13,23,43,79,139,257,467,863,1583,2909,5351,9839,18097,
%T A126273 33287,61223,112603,207113,380929,700643,1288657,2370223,4359517,
%U A126273 8018383,14748119,27126019,49892519,91766581,168785119,310444181
%N A126273 a(0) = a(1) = a(2) = 1, a(n) = largest prime <= a(n-1) + a(n-2) + a(n-3).
%C A126273 Analog of A055500 a(0)=1, a(1)=1, a(n) = largest prime <= a(n-1)+a(n-2). Might be called the Prime-tribonacci sequence. a(n) is asymptotic to c*T^n where T is the tribonacci constant 1.83928675 whose digits are A058265 for a real constant c.
%e A126273 a(3) = 3 = a(0)+a(1)+a(2) = 1+1+1 = 3.
%e A126273 a(4) = 5 = a(1)+a(2)+a(3) = 1+1+3 = 5.
%e A126273 a(5) = 7 < a(2)+a(3)+a(4) = 1+3+5 = 9.
%e A126273 a(6) = 13 < a(3)+a(4)+a(5) = 3+5+7 = 15.
%e A126273 a(7) = 23 < a(4)+a(5)+a(6) = 5+7+13 = 25.
%e A126273 a(8) = 43 = a(5)+a(6)+a(7) = 7+13+23 = 43.
%e A126273 a(9) = 79 = a(6)+a(7)+a(8) = 13+23+43 = 79.
%e A126273 a(10) = 139 < a(7)+a(8)+a(9) = 23+43+79 = 145.
%p A126273 a[0]:=1:a[1]:=1:a[2]:=1:for n from 3 to 40 do a[n]:=prevprime(1+a[n-1]+a[n-2]+a[n-3]) od: seq(a[n],n=0..40); # _Emeric Deutsch_, Mar 24 2007
%Y A126273 Cf. A000040, A000073, A055500, A058265.
%K A126273 easy,nonn
%O A126273 0,4
%A A126273 _Jonathan Vos Post_, Mar 09 2007
%E A126273 More terms from _Emeric Deutsch_, Mar 24 2007
%E A126273 Offset corrected by _N. J. A. Sloane_, Jun 16 2021