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A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.

%I A082454 #23 Jun 03 2022 11:17:48
%S A082454 0,0,5,3,9,9,15,15,21,21,31,29,39,39,45,45,55,57,63,65,73,71,81,81,91,
%T A082454 95,103,101,109,107,115,125,133,135,141,147,153,155,165,165,175,177,
%U A082454 183,189,195,195,201,209,225,225,231,231,241,239,253,255,265,267,273,275
%N A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.
%C A082454 In fact only one initial value is needed.
%C A082454 If initial values were {a(0)=0, a(1)=1} then we would get A014687.
%C A082454 prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 31 + 29 (order was reversed!).
%C A082454 If initial values were {a(0)=1, a(1)=2} then (after a(0)=1) we would get A000040, the primes, and would have prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 29 + 31 (identity).
%C A082454 Initial values {a(0)=1, a(1)=3} would give A014686.
%F A082454 a(n) = prime(n) + 2*(-1)^n. - _George Beck_, Jun 03 2022
%t A082454 g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=0; Table[g[w], {w, 0, 100}]
%t A082454 Prepend[Table[Prime[n] + 2 (-1)^n, {n, 59}],0] (* _George Beck_, Jun 03 2022 *)
%o A082454 (PARI) lista(nn) = {print1(a=0, ", "); print1(a, ", "); for (n=2, nn, a = prime(n) + prime(n-1) - a; print1(a, ", "););} \\ _Michel Marcus_, Apr 06 2015
%Y A082454 Cf. A000040, A014686, A014687, A082455.
%K A082454 nonn
%O A082454 0,3
%A A082454 _Labos Elemer_, Apr 25 2003
%E A082454 Name corrected by _George Beck_, Jun 03 2022